In this paper, a new extragradient algorithm is presented to solve the pseudomonotone equilibrium problem with a Bregman–Lipschitz-type condition. The superiority of this algorithm is that it can be performed without any precedent information about the Bregman–Lipschitz coefficients. The weak convergence of the algorithm is determinate under mild assumption, and the strong convergence will be established

Let G be a simple, connected graph and let A(G) be the adjacency matrix of G. If D(G) is the diagonal matrix of the vertex degrees of G, then for every real \(\alpha \in [0,1]\), the matrix \(A_{\alpha }(G)\) is defined as $$A_{\alpha }(G) = \alpha D(G) + (1- \alpha ) A(G).$$ The eigenvalues of the matrix \(A_{\alpha }(G)\) form the \(A_{\alpha }\)-spectrum of G. Let \(G_1 {\dot{\vee }} G_2\), \(G_1

A point p in projective plane is said to be quasi-Galois for a plane curve if the curve admits a non-trivial birational transformation which preserves the fibers of the projection \(\pi _p\) from the point p. A number of quasi-Galois points for smooth plane curves of degree d are studied. In this paper, we will study the relationship between dihedral groups and smooth plane curves with many quasi-Galois

A graph is NIC-planar if it can be drawn in the plane so that there is at most one crossing per edge and two pairs of crossing edges share at most one common end vertex. A (p, 1)-total k-labelling of a graph G is a function f from \(V(G)\cup E(G)\) to the color set \(\{0,1,\ldots ,k\}\) such that \(|f(x)-f(y)|\ge 1\) if \(xy\in E(G)\), \(|f(e_1)-f(e_2)|\ge 1\) if \(e_1\) and \(e_2\) are two adjacent

We study the inclusion relation of the triangular ratio metric balls and the Cassinian metric balls in subdomains of \(\mathbb {R}^n\). Moreover, we study distortion properties of Möbius transformations with respect to the triangular ratio metric in the punctured unit ball.

The exact solutions of the Riemann problem for a Temple-class hyperbolic system of conservation laws consisting of three scalar equations are obtained in fully explicit forms, in which all the state variables may contain Dirac delta functions simultaneously under some suitable Riemann initial data. The generalized Rankine–Hugoniot conditions and the over-compressive entropy condition are derived for

Let \(z_0\) and \(w_0\) be given points in the open unit disk \(\mathbb {D}\) with \(|w_0| < |z_0|\), and \(\mathcal {H}_0\) be the class of all analytic self-maps f of \(\mathbb {D}\) normalized by \(f(0)=0\). In this paper, we establish the third-order Dieudonné’s Lemma and apply it to explicitly determine the variability region \(\{f'''(z_0): f\in \mathcal {H}_0,f(z_0) =w_0, f'(z_0)=w_1\}\) for

The aim of this paper is to study the Wold-type decomposition in the class of m-isometries. One of our main results establishes an equivalent condition for an analytic m-isometry to admit the Wold-type decomposition for \(m\ge 2\). In particular, we introduce the k-kernel condition which we use to characterize analytic m-isometric operators which are unitarily equivalent to unilateral operator valued

In order to solve the general multidimensional perturbed oscillatory system \(y'' + \varOmega y = f(y, y')\) with \(K\in {\mathbb {R}}^{d\times d}\), the order conditions for the ERKN (extended Runge–Kutta–Nyström) methods and some effective ERKN methods were presented in the literature. These methods integrate exactly the multidimensional unperturbed oscillator \(y'' + \varOmega y = 0\). In this paper

In this work, we apply the extension of Mawhin’s coincidence degree theory by Ge and Ren to show existence of at least one solution to the nonlinear higher order p-Laplacian boundary value problems with integral boundary conditions on the half-line. The results obtained generalizes and compliments existing results in the literature. An example will be used to validate our result.

In this paper, we consider a nonlinear Schrödinger equation involving the fractional Laplacian with Dirichlet condition: $$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^{\frac{\alpha }{2}}u+A(x)u=f(x,u,\nabla u) \ \text{ in } \ \Omega ,\\ u>0, \ \text{ in }\ \Omega ; \ u\equiv 0, \ \text{ in }\ \mathbb R^n\backslash \Omega , \end{array}\right. } \end{aligned}$$ where \(\Omega \) is a domain

In this paper, we obtain the local regularity estimates in Besov spaces of weak solutions for the following parabolic p-Laplacian equations: $$\begin{aligned} u_{t}-\text {div} ~\! a \left( Du, x,t \right) =\text {div}~ {\mathbf {F}} \end{aligned}$$ under some proper assumptions on the functions a and \({\mathbf {F}}\). Moreover, we would like to point out that our results improve the known results

Let \({\mathscr {M}}\) be a semi-finite von Neumann algebra with a faithful normal semi-finite trace \(\tau \) and \(L^{p}({\mathscr {M}})\) the non-commutative \(L^p\) space associated with \(({\mathscr {M}},\tau )\). We extend star partial order \(\overset{*}{\le }\) and diamond order \(\le ^{\diamond }\) to \(L^{p}({\mathscr {M}})\) and present some properties about several bounds of these two partial

In this article, we consider the nonautonomous modified Swift–Hohenberg equation on infinite lattices. We first show the existence of a pullback-\({{\mathcal {D}}}\) attractor of the process generated by this equation. Then, we establish the existence of a unique family of invariant Borel probability measures carried by the pullback attractor. Finally, we construct statistical solutions for this equation

In this paper, we show the existence of the Lelong–Demailly numbers of positive S-plurisubharmonic currents. Moreover, a valid definition of \(\mathrm{{dd}}^{c}g \wedge T\) is obtained for plurisubharmonic currents T and unbounded plurisubharmonic functions g. The importance of this definition comes from the sharpness of our condition on the Hausdorff dimension of the locus points of g.

This paper investigates a single server queueing system with an infinite waiting space in which customers are arrived according to renewal process and are served in batches of random size under continuous-time batch Markovian service process. We first determine the vector probability generating function of the system-length distribution at pre-arrival epoch. The system-length distribution at pre-arrival

In this paper, we give a description of Lie (Jordan) triple derivations and generalized Lie (Jordan) triple derivations of an arbitrary triangular algebra \({\mathfrak {A}}\) through a triangular algebra \({\mathfrak {A}}^{0},\) where \({\mathfrak {A}}^{0}\) is a triangular algebra constructed from the given triangular algebra \({\mathfrak {A}}\) using the notion of maximal left (right) ring of quotients

Let \(w=(w_0,w_1, \dots ,w_l)\) be a vector of nonnegative integers such that \( w_0\ge 1\). Let G be a graph and N(v) the open neighbourhood of \(v\in V(G)\). We say that a function \(f: V(G)\longrightarrow \{0,1,\dots ,l\}\) is a w-dominating function if \(f(N(v))=\sum _{u\in N(v)}f(u)\ge w_i\) for every vertex v with \(f(v)=i\). The weight of f is defined to be \(\omega (f)=\sum _{v\in V(G)} f(v)\)

The Wiener index is one of the most widely studied parameters in chemical graph theory. It is defined as the sum of the lengths of the shortest paths between all unordered pairs of vertices in a given graph. In 1991, Šoltés posed the following problem regarding the Wiener index: Find all graphs such that its Wiener index is preserved upon removal of any vertex. The problem is far from being solved

The number of spanning trees of a graph G is the total number of distinct spanning subgraphs of G that are trees. Feng et al. determined the maximum number of spanning trees in the class of connected graphs with n vertices and matching number \(\beta \) for \(2\le \beta \le n/3\) and \(\beta =\lfloor n/2\rfloor \). They also pointed out that it is still an open problem to the case of \(n/3<\beta \le

Let \(G=(V(G),E(G))\) be a simple graph. A set \(S \subseteq V(G)\) is a strong edge geodetic set if there exists an assignment of exactly one shortest path between each pair of vertices from S, such that these shortest paths cover all the edges E(G). The cardinality of a smallest strong edge geodetic set is the strong edge geodetic number \(\mathrm{sg_e}(G)\) of G. In this paper, the strong edge geodetic

The connective eccentricity index is a degree-distance-based graph invariant, while the modified second Zagreb index is a degree-based graph invariant. The Parikh word representable graph is a new class of graphs G(w), which corresponds to words w that are finite sequence of symbols. In this paper, we first present explicit formulas for the connective eccentricity index and modified second Zagreb index

The Mostar index of a graph was defined by Došlić, Martinjak, Škrekovski, Tipurić Spužević and Zubac in the context of the study of the properties of chemical graphs. It measures how far a given graph is from being distance-balanced. In this paper, we determine the Mostar index of two well-known families of graphs: Fibonacci cubes and Lucas cubes.

This paper is concerned with the large time decay rates of the two-dimensional (2D) micropolar equations with zero angular viscosity. Based on the generalized Fourier splitting methods and low frequency effect analysis, we firstly obtain the solutions decay as \(\Vert u\Vert _{L^2}+ \Vert \omega \Vert _{L^2}\le C(1+t)^{-\frac{1}{2}}\). Moreover, by exploring the new structure of the system, we obtain

Given a finite graph G, the maximum length of a sequence \((v_1,\ldots ,v_k)\) of vertices in G such that each \(v_i\) dominates a vertex that is not dominated by any vertex in \(\{v_1,\ldots ,v_{i-1}\}\) is called the Grundy domination number, \(\gamma _\mathrm{gr}(G)\), of G. A small modification of the definition yields the Z-Grundy domination number, which is the dual invariant of the well-known

A central vertex of a graph is a vertex whose eccentricity equals the radius. The center of a graph is the set of all central vertices. The central ratio of a graph is the ratio of the cardinality of its center to its order. In 1982, Buckley proved that every positive rational number not exceeding one is the central ratio of some graph. In this paper, we obtain more detailed information by determining

The \(\tau \)-Keiper/Li coefficients attached to a function F are closely related to its zero-free regions. However, the absence of a closed formula for calculating these coefficients makes them challenging to use. Motivated by Voros approach, we introduce the discretized \(\tau \)-Keiper/Li coefficients. A finite sum representation derived for these coefficients is useful for numerical calculations

The exact solutions to the Riemann problem for an inhomogeneous extended Chaplygin gas equations with friction are constructed explicitly. Compared to the homogeneous system, the Riemann solutions for the inhomogeneous one are no longer self-similar. Then, as the two exponents vanish wholly or partly, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock

We study the existence and asymptotic behavior of least energy sign-changing solutions for a N-Laplacian equation of Kirchhoff type with critical exponential growth in \(\mathbb {R}^N\)$$\begin{aligned} \left\{ \begin{aligned}&- \bigg (a+b\int _{\mathbb {R}^N}|\nabla u|^N\mathrm{d}x\bigg )\Delta _N u+V(|x|) |u|^{N-2}u= f(|x|,u), \\&u\in W^{1,N}(\mathbb {R}^N), \\ \end{aligned} \right. \end{aligned}$$

In this paper, we give some vanishing theorems for harmonic p-forms on complete noncompact Riemannian manifolds satisfying a weighted p-Poincaré inequality with nonnegative scalar curvature and under pointwise curvature pinching conditions which are bounded from above by the weight function.

This paper investigates the nonlinear backward fractional diffusion equations (BFDEs) having a variable order and variable diffusion coefficient. It is well-known that the BFDEs are ill-posed in the sense of Hadamard. Moreover, we investigate the problem taking into account the disturbance both variable diffusion coefficient and variable order. This may lead to some common regularization strategy to

The commuting graph \(\varDelta (G)\) of a finite non-abelian group G is a simple graph with vertex set G, and two distinct vertices x, y are adjacent if \(xy = yx\). In this paper, first we discuss some properties of \(\varDelta (G)\). We determine the edge connectivity and the minimum degree of \(\varDelta (G)\) and prove that both are equal. Then, other graph invariants, namely: matching number

In this work, we look at the extension of classical discrete dynamical system to multidimensional discrete-time dynamical system by characterizing chaos notions on \({\mathbb {Z}}^d\)-action. The \({\mathbb {Z}}^d\)-action on a space X has been defined in a very general manner, and therefore we introduce a \({\mathbb {Z}}^d\)-action on X which is induced by a continuous map, \(f:{\mathbb {Z}}\times

The paper proposes a new explicit extragradient algorithm for solving an equilibrium problem over the solution set of another generalized equilibrium problem which usually is called bilevel equilibrium problems in a real Hilbert space. The algorithm combines extragradient methods with auxiliary problem techniques. Theorem of the strong convergence of the algorithm is established under standard assumptions

The key goal of this article is to propose a modification of certain exponential type operators defined by Ismail and May. Particularly, we concentrate on a sequence of operators that preserve \(e^{-x}\) and constant functions. We find the moments of these modified operators using the concept of moment generating function with the help of Mathematica software. We show uniform convergence of these modified

The independence polynomial of a graph G is \(I(G;x)=\sum _{k=0}^{\alpha (G)} s_{k}\cdot x^{k}\), where \(s_{k}\) and \(\alpha (G)\) denote the number of independent sets of cardinality k and the independence number of G, respectively. We say that a cycle is a \(\tilde{3}\)-cycle if its length is divisible by 3, otherwise a non-\(\tilde{3}\)-cycle. Define \(\phi (G)\) to be the decycling number of

In the present work, we investigate infinite horizon optimal control problems driven by a class of stochastic delay evolution equations in Hilbert spaces and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation (ABSEE). We first establish a priori estimate for the solution to ABSEEs by imposing restriction on unbounded operator \(A^*\), that is, the operator

We consider almost Riemann solitons \((V,\lambda )\) in a Riemannian manifold and underline their relation to almost Ricci solitons. When V is of gradient type, using Bochner formula, we explicitly express the function \(\lambda \) by means of the gradient vector field V and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential

In the present work, we investigate the global existence and uniform decay rates of solutions to the Cauchy problem in \(\mathbf {R}^{n}\) (\(n\ge 1)\) related to the dynamic behavior of evolution equations accounting for rotational inertial forces along with a linear viscoelastic memory damping arising in viscoelastic materials. Under certain conditions on the initial data and on the kernel, the global

Let \(\mathcal {L}_2=(-\Delta )^2+V^2 \) be the Schrödinger-type operator on \(\mathbb {R}^n (n\ge 5),\) where the nonnegative potential \(V\) belongs to the reverse Hölder class \(RH_s, n/2

In this paper, we study the concomitants of m-generalized order statistics (m-GOSs) and m-dual generalized order statistics (m-DGOSs) from bivariate Cambanis family with nonzero parameter values as an extension of several recent papers. Moreover, we derive some information measures, namely the Shannon entropy, Kullback–Leibler (KL) divergence and Fisher information number (FIN) for the concomitants

We consider discrete Sturm–Liouville-type equations of the form $$\begin{aligned} \varDelta (r_n\varDelta x_n)=a_nf(x_{\sigma (n)})+b_n. \end{aligned}$$ We present a theory of asymptotic properties of solutions which allows us to control the degree of approximation. Namely, we establish conditions under which for a given sequence y which solves the equation \(\varDelta (r_n\varDelta y_n)=b_n\), the

We define and analyze the k-directional short-time Fourier transform and its synthesis operator over Gelfand–Shilov spaces \(\mathcal {S}^\alpha _{\beta }(\mathbb {R}^n)\) and \(\mathcal {S}^\alpha _{\beta }({\mathbb {R}}^{k+n})\), respectively, and their duals. Also, we investigate directional regular sets and their complements—directional wave fronts, for elements of \(\mathcal {S}^{\prime \alpha

We consider a reaction–diffusion equation on a 3D thin porous media of thickness \(\varepsilon \) which is perforated by periodically distributed cylinders of size \(\varepsilon \). On the boundary of the cylinders, we prescribe a dynamical boundary condition of pure-reactive type. As \(\varepsilon \rightarrow 0\), in the 2D limit the resulting reaction–diffusion equation has a source term coming from

In this paper, we prove that if a nonconstant finite order meromorphic function f and its n-th order difference operator \(\Delta ^n_{\eta }f\) share \(a_1,\) \(a_2,\) \(a_3\) CM, where n is a positive integer, \(\eta \ne 0\) is a finite complex value, and \(a_1,\) \(a_2,\) \(a_3\) are three distinct finite complex values, then \(f(z)=\Delta ^n_{\eta }f(z)\) for each \(z\in \mathbb {C}.\) The main

In this paper, we present some new identities for multiple polylogarithm functions by using the methods of iterated integral computations of logarithm functions. Then, by applying these formulas obtained, we establish several duality formulas for Arakawa–Kaneko zeta values and Kaneko–Tsumura \(\eta \)-values. At the end of the paper, we study a variant of Kaneko–Tsumura \(\eta \)-function with r-complex

We study hypersurfaces in the pseudo-Euclidean space, whose mean curvature vector satisfies the equation: Laplacian of the vector is parallel to the vector (with constant factor), and the second fundamental form has constant norm. We prove that every such hypersurface of diagonalizable shape operator with at most six distinct principal curvatures has constant mean curvature and constant scalar curvature

The class of \(\{P_1,P_2\}\)-Nekrasov matrices, defined in terms of permutation matrices \(P_1\) and \(P_2\), is a generalization of the well-known class of Nekrasov matrices. In this paper, some computable error bounds for linear complementarity problems (LCPs) of \(\{P_1,P_2\}\)-Nekrasov matrices are given, which depend only on the entries of the involved matrices and can be used to obtain the perturbation

For a connected graph G and \(a,b \in \mathbb {R}\), the general degree-eccentricity index is defined as \(\mathrm{DEI}_{a,b}(G) = \sum _{v \in V(G)} d_{G}^{a}(v) \mathrm{ecc}_{G}^{b}(v)\), where V(G) is the vertex set of G, \(d_{G} (v)\) is the degree of a vertex v and \(\mathrm{ecc}_{G}(v)\) is the eccentricity of v in G. We obtain sharp upper and lower bounds on the general degree-eccentricity index

In this paper, an SEIRS epidemic model is proposed, incorporating appropriate compartments as isolated exposed class and diagnosed class, relevant to interventions. In the scenario of constant isolated proportion, the qualitative analyses are carried out in terms of the basic reproduction number \(\mathscr {R}_0\). The sensitivity of \(\mathscr {R}_0\) with respect to model parameters is discussed

Let R be a noncommutative prime ring of characteristic different from 2 and 3, C the extended centroid of R, F and G two generalized derivations of R, d a nonzero derivation of R and \(f(x_1,\ldots ,x_n)\) a multilinear polynomial over C. Suppose that I is a nonzero ideal of R and \(f(I)=\{f(x_1,\ldots ,x_n)| x_1,\ldots ,x_n\in I\}\). If \(f(x_1,\ldots ,x_n)\) is not central valued on R and $$\begin{aligned}

The Bohr radius for a class \({\mathcal {G}}\) consisting of analytic functions \(f(z)=\sum _{n=0}^{\infty }a_nz^n\) in unit disc \({\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1\}\) is the largest \(r^*\) such that every function f in the class \({\mathcal {G}}\) satisfies the inequality $$\begin{aligned} d\left( \sum _{n=0}^{\infty }|a_nz^n|, |f(0)|\right) = \sum _{n=1}^{\infty }|a_nz^n|\le d(f(0), \partial

The aim of this paper is to show that fixed point theorem in cones can be applied to singular equations. Using the positivity of Green’s function and the external force e(t), we prove the existence of a positive periodic solution for a damped singular equation with sub-linearity, semi-linearity and super-linearity conditions, and these results are applicable to weak and strong singularities. As applications

In this paper, the products of modified Bessel functions of the first kind are considered. Our main aim is to provide various conditions so that these products have certain geometric properties such as starlikeness, convexity, and close to convexity (univalency) with respect to certain functions in the unit disk. Subordinating factor sequences for these products are also obtained. Interesting consequences

In this paper, we prove global existence of strong solutions to the 2D density-dependent incompressible magnetic Bénard problem in a bounded domain.

In this work, we estimate the bounds for the logarithmic coefficients \(\gamma _n\) of some well-known classes like \({\mathcal {F}}(c)\) for \(c\in (0,0.656]\cup \{2\}\). The best bound obtained for the logarithmic coefficient \(|\gamma _5|\) is sharp for \(c=2\). In a special case, it is important to note that we obtain the bounds for the logarithmic coefficients \(\gamma _n\) of the convex functions

In 2011, Gross derived an \(O(n^2)\)-time algorithm to calculate the genus distribution of a given cubic Halin graph. In this paper, with the help of the overlap matrix, we obtain a recurrence relation for the Euler-genus polynomials of cubic caterpillar-Halin graphs. Explicit formulas for the embeddings of the cubic caterpillar-Halin graphs into surfaces with Euler-genus 0, 1 and 2 are also obtained

In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if \(\beta (G)\) denotes the metric dimension of a maximal outerplanar graph G of order n, we prove that \(2\le \beta (G) \le \lceil \frac{2n}{5}\rceil \) and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of G is 2 and to build a resolving set S of size

The present paper deals with a generalization of the Baskakov type operators, which preserve an exponential function and approximate functions with arbitrary order. We give some direct results including error estimation and quantitative asymptotic formula. It is observed that the rate of approximation can be made smaller by arbitrarily chosen sequences.

In this paper, we study ad-nilpotent elements in Lie algebras arising from semiprime associative rings R free of 2-torsion. With the idea of keeping under control the torsion of R, we introduce a more restrictive notion of ad-nilpotent element, pure ad-nilpotent element, which is a only technical condition since every ad-nilpotent element can be expressed as an orthogonal sum of pure ad-nilpotent elements