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A novel comprehensive analysis on generalized harmonically ψ-convex with respect to Raina's function on fractal set with applications
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-04-26 , DOI: 10.1002/mma.7346
Yu‐ming Chu 1 , Saima Rashid 2 , Jagdev Singh 3
Affiliation  

The pivotal proposal of this work is to present a new class of harmonically convex functions, namely, generalized harmonically ψ-convex functions based on the fractal set technique for establishing inequalities of Hermite–Hadamard type, Pachpatte type, and certain related variants with respect to the Raina's function. With the aid of an auxiliary identity correlated with Raina's function, by generalized Hölder inequality, two Hermite–Hadamard-type local fractional integral inequalities for generalized harmonically ψ-convex functions are apprehended. The proposed technique provides the results by giving some special values to the parameters or imposing restrictive assumptions and is completely feasible for recapturing the existing results in the relative literature. To determine the computational efficiency of offered scheme, some numerical applications are discussed. The results of the scheme show that the approach is straightforward to apply and computationally very user-friendly and accurate.

中文翻译:

分形集上关于Raina函数的广义调和ψ-凸综合分析及其应用

这项工作的关键建议是提出一类新的调和凸函数,即基于分形集技术的广义调和ψ -凸函数,用于建立 Hermite-Hadamard 型、Pachpatte 型和某些相关变体的不等式Raina 的功能。借助与 Raina 函数相关的辅助恒等式,通过广义 Hölder 不等式,广义调和ψ的两个 Hermite-Hadamard 型局部分数阶积分不等式-凸函数被理解。所提出的技术通过为参数赋予一些特殊值或施加限制性假设来提供结果,并且对于重新获得相关文献中的现有结果是完全可行的。为了确定所提供方案的计算效率,讨论了一些数值应用。该方案的结果表明,该方法应用简单,计算上非常用户友好和准确。
更新日期:2021-04-26
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