Some new inequalities for n-polynomial s-type convexity pertaining to inter-valued functions governed by fractional calculus

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-10-19 DOI:10.1142/s0218348x23401989

Zareen A. Khan, Humaira Kalsoom

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引用次数: 0

Abstract

The main goals of this paper are to provide an introduction to the idea of interval-valued [Formula: see text]-polynomial [Formula: see text]-type convex functions and to investigate the algebraic properties of this type of function. This new generalization aims to show the existence of new Hermite–Hadamard inequalities for the recently presented class of interval-valued [Formula: see text]-polynomials of [Formula: see text]-type convex describing the [Formula: see text]-fractional integral operator. In the classical sense, some special cases are figured out, and the two examples are also given. There are some recently discovered inequalities for interval-valued functions that are regulated by fractional calculus applicable to interval-valued [Formula: see text]-polynomial [Formula: see text]-type convexity. The results obtained show that future research will be simple to implement, highly efficient, feasible, and extremely precise in its investigation. It could also help solve modeling problems, optimization problems, and fuzzy interval-valued functions that involve both discrete and continuous variables.

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关于分数阶微积分控制的间值函数的n多项式s型凸性的几个新不等式

本文的主要目的是介绍区间值[公式:见文]-多项式[公式:见文]型凸函数的思想，并研究这类函数的代数性质。这一新的推广旨在证明最近提出的一类区间值[公式:见文]-描述[公式:见文]-分数积分算子的[公式:见文]-型凸的多项式-新的Hermite-Hadamard不等式的存在性。在经典意义上，指出了一些特殊情况，并给出了两个例子。最近发现了一些由分数阶微积分调节的区间值函数的不等式，这些不等式适用于区间值[公式:见文]-多项式[公式:见文]型凸性。结果表明，未来的研究将是简单、高效、可行和极其精确的调查。它还可以帮助解决建模问题、优化问题以及涉及离散变量和连续变量的模糊区间值函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.