In this paper, we study the structure of the discrete Muckenhoupt class $\mathcal{A}^{p}(\mathcal{C})$ and the discrete Gehring class $\mathcal{G}^{q}(\mathcal{K})$ . In particular, we prove that the self-improving property of the Muckenhoupt class holds, i.e., we prove that if $u\in \mathcal{A}^{p}(\mathcal{C})$ then there exists $q< p$ such that $u\in \mathcal{A}^{q}(\mathcal{C}_{1})$ . Next, we

In this paper, we consider the initial boundary value problem of two-dimensional isentropic compressible Boussinesq equations with constant viscosity and thermal diffusivity in a square domain. Based on the time-independent lower-order and time-dependent higher-order a priori estimates, we prove that the classical solution exists globally in time provided the initial mass $\|\rho _{0}\|_{L^{1}}$ of

The aim of this paper is computing the coderivatives of efficient point and efficient solution set-valued maps in a parametric vector optimization problem. By using a method different from the existing literature we establish an upper estimate and explicit expression for the coderivatives of an efficient point set-valued map where the independent variable can take values in the whole space. As an application

The aim of this study is to introduce the notion of two-dimensional approximately harmonic $(p_{1},h_{1})$ - $(p_{2},h_{2})$ -convex functions. We show that the new class covers many new and known extensions of harmonic convex functions. We formulate several new refinements of Hermite–Hadamard like inequalities involving two-dimensional approximately harmonic $(p_{1},h_{1})$ - $(p_{2},h_{2})$ -convex

The main objective of this paper is to derive a new post quantum integral identity using twice $(p,q)$ -differentiable functions. Using this identity as an auxiliary result, we obtain some new post quantum estimates of upper bounds involving twice $(p,q)$ -differentiable preinvex functions.

In this paper, we introduce a modified Krasnoselski–Mann type iterative method for capturing a common solution of a split mixed equilibrium problem and a hierarchical fixed point problem of a finite collection of k-strictly pseudocontractive nonself-mappings. Many of the algorithms for solving the split mixed equilibrium problem involve a step size which depends on the norm of a bounded linear operator

Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special numbers and polynomials. In recent years, studying degenerate versions regained lively interest of some mathematicians. The purpose of this paper is to study degenerate Bell polynomials by using umbral calculus and generating functions. We derive several

The aim of this paper is to study the unsigned degenerate r-Stirling numbers of the first kind as degenerate versions of the r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind as those of the r-Stirling numbers of the second kind. For the degenerate r-Stirling numbers of both kinds, we derive recurrence relations, generating functions, explicit expressions

This paper deals with solvability and algorithms for a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By employing the Banach’s fixed point theorem, Schauder’s fixed point theorem, and FanKKM theorem, we obtain a sufficient condition which guarantees the existence of solutions for the generalized nonlinear variational-like inequality. We introduce also

In this paper, we focus on the response mean of the partially linear varying-coefficient errors-in-variables model with missing response at random. A simulation study is conducted to compare jackknife empirical likelihood method with normal approximation method in terms of coverage probabilities and average interval lengths, and a comparison of the proposed estimators is done based on their biases

In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao

The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability

This paper is to consider the unity results on entire functions sharing two values with their difference operators and to prove some results related to 4 CM theorem. The main result reads as follows: Let $f(z)$ be a nonconstant entire function of finite order, and let $a_{1}$ , $a_{2}$ be two distinct finite complex constants. If $f(z)$ and $\Delta _{\eta }^{n}f(z)$ share $a_{1}$ and $a_{2}$ “CM”,

We investigate some new topological properties of the multiplication operator on $C(p)$ defined by Lim (Tamkang J. Math. 8(2):213–220, 1977) equipped with the pre-quasi-norm and the pre-quasi-operator ideal formed by this sequence space and s-numbers.

The Editor-in-Chief has retracted this article [1] because it significantly overlaps with previously published articles [2, 3] and an article by another author that was simultaneously under consideration at another journal [4]. The article also shows evidence of authorship manipulation. In addition, the identity of the third author could not be verified: the University of Delaware have confirmed that

With the increasing availability of spatially extensive geo-referenced data, much attention has been paid to the use of local statistics to identify local patterns of spatial association, in which the null distributions of local statistics play an essential role in the related statistical inference. As a powerful tool to approximate the distribution of a statistic, the bootstrap method is used in this

Wavelets are particularly useful because of their natural adaptive ability to characterize data with intrinsically local properties. When the data contain outliers or come from a population with a heavy-tailed distribution, $L_{1}$ -estimation should obtain a better fit. In this paper, we propose a $L_{1}$ -wavelet method for nonparametric regression, and derive the asymptotic properties of the $L_{1}$

In this work, we deal with the blow-up solutions of the following parabolic p-Laplacian equations with a gradient source term: $$ \textstyle\begin{cases} (b(u) )_{t} =\nabla \cdot ( \vert \nabla u \vert ^{p-2}\nabla u )+f(x,u, \vert \nabla u \vert ^{2},t) &\text{in } \varOmega \times (0,t^{*}), \\ \frac{\partial u}{\partial n}=0 &\text{on } \partial \varOmega \times (0,t^{*}),\\ u(x,0)=u_{0}(x)\geq

In this paper, a primal–dual interior point QP-free algorithm for mathematical programs with complementarity constraints is presented. Firstly, based on Fischer–Burmeister function and smoothing techniques, the investigated problem is approximated by a smooth nonlinear constrained optimization problem. Secondly, combining with an effective penalty function technique and working set, a QP-free algorithm

In this paper, we study the alternating CQ algorithm for solving the split equality problem in Hilbert spaces. It is, however, not easy to implement since its selection of the stepsize requires prior information on the norms of bounded linear operators. To avoid this difficulty, we propose several modified algorithms in which the selection of the stepsize is independent of the norms. In particular

In this paper, firstly, we prove a Jensen–Mercer inequality for GA-convex functions. After that, we establish weighted Hermite–Hadamard’s inequalities for GA-convex functions using the new Jensen–Mercer inequality, and we establish some new inequalities connected with Hermite–Hadamard–Mercer type inequalities for differentiable mappings whose derivatives in absolute value are GA-convex.

This manuscript aims to initiate some recent theoretical consequences related to tripled coincidence points for non-self mappings via the notion of C-type functions in partially ordered complete metric-like space (for short, POCML space). Our contributions unify and expand some previous studies in this line. Moreover, some corollaries and suitable examples are presented to demonstrate the novelty of

In this paper, we obtain some isoperimetric inequalities for the first $(n-1)$ eigenvalues of the fourth order Neumann Laplacian on bounded domains in an n-dimensional Euclidean space. Our result supports strongly the conjecture of Chasman.

The main goal of this paper is to set up some new estimates of a specific class of dynamic integral inequalities (DII) which are partially linear on a time scale $\mathbb{T}$ with two independent variables. These, from the one hand, sum up and, on the other hand, offer a helpful method for both the qualitative and quantitative study of dynamic equations on time scales. Some applications are taken into

In this paper, we establish certain generalized fractional integral inequalities of mean and trapezoid type for $(s+1)$ -convex functions involving the $(k,s)$ -Riemann–Liouville integrals. Moreover, we develop such integral inequalities for h-convex functions involving the k-conformable fractional integrals. The legitimacy of the derived results is demonstrated by plotting graphs. As applications

Spacelike submanifolds usually appear in the study of questions related to causality in general relativity. In this paper, we study an n-dimensional spacelike submanifold in $(n + p)$ -dimensional connected de Sitter space $S^{n+p}_{q}(c)$ of index q ( $1\leq q \leq p$ ) and of constant curvature c, and we obtain some integral inequalities of Simons type and rigidity theorems.

This paper studies fractional integral inequalities for fractional integral operators containing extended Mittag-Leffler (ML) functions. These inequalities provide upper bounds of left- and right-sided fractional integrals for $(\alpha, h-m)$ convex functions. A generalized fractional Hadamard inequality is established. All the results hold for h-convex, $(h, m)$ -convex, $(\alpha, m)$ -convex, $(s

This paper presents an extragradient-like method for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition on Hadamard manifolds. The algorithm only needs to know the existence of the Lipschitz-type constants of the bifunction, and the stepsize of each iteration is determined by the adjacent iterations. Convergence of the algorithm is analyzed, and its application to variational

This research focuses on proving the results of tripled fixed point and coincidence point in generalized metric spaces endowed with vector-valued metrics and matrix equations. The results from this study are illustrated by two applications.

In this paper, we discuss the q-Laplace-type integral operator on certain class of special functions. We propose q-analogues and obtain results involving polynomials of even orders and functions of q-trigonometric types. Moreover, we establish results related to q-hyperbolic functions and certain q-differential operators. Relying on the given q-differentiation formulas, we finally derive the nth derivative

The aim of this paper is to establish the boundednes of the commutator $[b,T_{\alpha }]$ generated by θ-type generalized fractional integral $T_{\alpha }$ and $b\in \widetilde{\mathrm{RBMO}}(\mu )$ over a non-homogeneous metric measure space. Under the assumption that the dominating function λ satisfies the ϵ-weak reverse doubling condition, the author proves that the commutator $[b,T_{\alpha }]$ is

Hypersingular integrals have appeared as effective tools for inversion of multidimensional potential-type operators such as Riesz, Bessel, Flett, parabolic potentials, etc. They represent (at least formally) fractional powers of suitable differential operators. In this paper the family of the so-called “truncated hypersingular integral operators” $\mathbf{D}_{\varepsilon }^{\alpha }f$ is introduced

We prove a generalized Hölder-type inequality for measurable operators associated with a semi-finite von Neumann algebra which is a generalization of the result shown by Bekjan (Positivity 21:113–126, 2017). This also provides a generalization of the unitarily invariant norm inequalities for matrix due to Bhatia–Kittaneh, Horn–Mathisa, Horn–Zhan and Zou under a cohyponormal condition.

In this paper, the criterion that points of Orlicz function spaces equipped with Φ-Amemiya norm generated by an Orlicz function are strongly extreme is given. As a corollary, the sufficient and necessary conditions of midpoint local uniform rotundity of Orlicz function spaces equipped with Φ-Amemiya norm are obtained.

Kayal (Probab. Eng. Inf. Sci. 30(4):640–662, 2016) first proposed generalized cumulative entropy based on lower record values. Motivated by Kayal (Probab. Eng. Inf. Sci. 30(4):640–662, 2016), recently, Tahmasebi and Eskandarzadeh (Stat. Probab. Lett. 126:164–172, 2017) proposed an extended cumulative entropy (ECE) based on kth lower record values. In this paper, we obtain some properties of ECE. We

Let $\Re_{I}(m,n)$ be the first Cartan domain. Motivated by some results of the multiplication operators on the holomorphic function spaces on the unit ball of ${\mathbb {C}}^{n}$ , we study multiplication operators on weighted Bloch spaces of the first Cartan domain and obtain some necessary or sufficient conditions for the boundedness and compactness in this paper.

This paper focuses on a class of hider-order nonlinear fractional boundary value problems. The boundary conditions contain Riemann–Stieltjes integral and nonlocal multipoint boundary conditions. It is worth mentioning that the nonlinear term and the boundary conditions contain fractional derivatives of different orders. Based on the Schauder fixed point theorem, we obtain the existence of solutions

In this paper, we introduce Bregman subgradient extragradient methods for solving variational inequalities with a pseudo-monotone operator which are not necessarily Lipschitz continuous. Our algorithms are constructed such that the stepsizes are determined by an Armijo line search technique, which improves the convergence of the algorithms without prior knowledge of any Lipschitz constant. We prove

This paper deals with a class of high-order inertial Hopfield neural networks involving mixed delays. Utilizing differential inequality techniques and the Lyapunov function method, we obtain a sufficient assertion to ensure the existence and global exponential stability of anti-periodic solutions of the proposed networks. Moreover, an example with a numerical simulation is furnished to illustrate the

In this paper, we obtain the existence and boundedness of Marcinkiewicz integrals with homogeneous kernels on central Campanato spaces. Moreover, the existence and boundedness of multilinear Marcinkiewicz integrals on central Campanato spaces are also deduced. We extend various previous results to central Campanato spaces which can be seen as the local version of Campanato spaces.

This paper concerns the long term behavior of the stochastic two-dimensional g-Navier–Stokes equations with additive noise defined on a sequence of expanding domains, where the ultimate domain is unbounded and of Poincaré type. We prove that the weak continuity is uniform with respect to all expanding cocycles, which yields the equi-asymptotic compactness by using an energy equation method. Finally

This paper is devoted to obtain generalized results related to majorization-type inequalities by using well-known Fink’s identity and new types of Green functions, introduced by Mehmood et al. (J. Inequal. Appl. 2017:108, 2017). We give a generalized majorization theorem for the class of n-convex functions. We utilize the Csiszár f-divergence and generalized majorization-type inequalities in providing

The aim of this paper is to establish new generalized fractional versions of the Hadamard and the Fejér–Hadamard integral inequalities for harmonically convex functions. Fractional integral operators involving an extended generalized Mittag-Leffler function which are further generalized via a monotone increasing function are utilized to get these generalized fractional versions. The results of this

By providing a new iterative method our aim is finding a common element of the set of fixed points of two nonexpansive mappings, the set of solutions to a variational inclusion and the set of solutions of a generalized equilibrium problem in a real Hilbert space. We review the strong convergence of the new iterative method in the framework of Hilbert spaces. Finally, we show that our main result is

In this paper, we introduce a new extension of the double controlled metric-type spaces, called double controlled metric-like spaces, by assuming that the “self-distance” may not be zero On the other hand, if the value of the metric is zero, then it has to be a “self-distance” (i.e., we replace $[\varsigma(g,h)=0 \Leftrightarrow g=h]$ by $[\varsigma(g,h)=0 \Rightarrow g=h]$ ). Using this new type of

M-eigenvalues of elasticity M-tensors play an important role in nonlinear elasticity and materials. In this paper, we present several new lower bounds for the minimum M-eigenvalue of elasticity M-tensors and propose numerical examples to illustrate the efficiency of the obtained results. As applications, we provide several checkable sufficient conditions for the strong ellipticity and positive definiteness

In this paper, we estimate the best wavelet approximations of a function f having bounded second derivatives and bounded higher-order derivatives using Chebyshev wavelets of third and fourth kinds.

In this paper, we investigate the exponential mean-square stability for both the solution of n-dimensional stochastic delay integro-differential equations (SDIDEs) with Poisson jump, as well for the split-step θ-Milstein (SSTM) scheme implemented of the proposed model. First, by virtue of Lyapunov function and continuous semi-martingale convergence theorem, we prove that the considered model has the

The aim of this present investigation is establishing Minkowski fractional integral inequalities and certain other fractional integral inequalities by employing the Marichev–Saigo–Maeda (MSM) fractional integral operator. The inequalities presented in this paper are more general than the existing classical inequalities cited.

In this paper, we introduce blending functions of Lupaş q-Bernstein operators with shifted knots for constructing q-Bézier curves and surfaces. We study the nature of degree elevation and degree reduction for Lupaş q-Bézier Bernstein functions with shifted knots for $t \in [\frac{a}{[\mu ]_{q}+b} , \frac{[\mu ]_{q}+a}{[\mu ]_{q}+b} ]$ . For the parameters $a=b=0$ , we get Lupaş q-Bézier curves defined

In this paper, we consider the existence of nontrivial solutions for a fractional p-q Laplacian equation with critical nonlinearity in a bounded domain. Our approach is based on variational methods and some analytical techniques.

In this paper, we consider the linear fractional differential equation By obtaining the Green’s function we derive the Lyapunov-type inequality for such a boundary value problem. Furthermore, we use the contraction mapping theorem to study the existence of a unique solution for the corresponding nonlinear problem.

In this paper, we prove weighted norm inequalities for vector-valued multilinear singular integrals with nonsmooth kernels and commutators on generalized weighted Morrey space.

A number of families of q-extensions of analytic functions in the open unit disk $\mathbb{U}$ have been defined by means of basic (or q-)calculus and considered from many distinctive prospectives and viewpoints. In this paper, we generalize and study certain subclasses of analytic functions involving higher-order q-derivative operators. We settle characteristic equations for these presumably new classes

The aim of the present paper is to study radii problems for two general classes including various known subclasses of analytic functions associated with the normalized form of Legendre polynomials of odd degree. We also obtain some special cases of the main results presented here with some useful examples.

This paper gives some novel generalizations by considering the generalized conformable fractional integrals operator for reverse Minkowski type and reverse Hölder type inequalities. Furthermore, novel consequences connected with this inequality, together with statements and confirmation of various variants for the advocated generalized conformable fractional integral operator, are elaborated. Moreover

We present new generalizations of the weighted Montgomery identity constructed by using the Hermite interpolating polynomial. The obtained identities are used to establish new generalizations of weighted Ostrowski type inequalities for differentiable functions of class $C^{n}$ . Also, we consider new bounds for the remainder of the obtained identities by using the Chebyshev functional and certain Grüss

In this paper, some new inequalities of the Hermite–Hadamard type for the classes of functions whose derivatives’ absolute values are m-convex and $( \alpha , m) $-convex are obtained. The results obtained in this work extend and improve the corresponding ones in the literature. Some applications to special means of real numbers are also given.

A classical result in random matrix theory reveals that the limiting spectral distribution of a Wigner matrix whose entries have a common variance and satisfy other regular assumptions almost surely converges to the semicircular law. In the paper, we will relax the assumption of uniform covariance of each entry, when the average of the normalized sums of the variances in each row of the data matrix

Let $T_{a,\varphi }$ be a Fourier integral operator with symbol a and phase φ. In this paper, under the conditions $a(x,\xi )\in L^{\infty }S^{n(\rho -1)/2}_{\rho }(\omega )$ and $\varphi \in L^{\infty }\varPhi ^{2}$, the authors show that $T_{a,\varphi }$ is bounded from $L^{2}(\mathbb{R}^{n})$ to $L^{2}(\mathbb{R}^{n})$.