Some novel estimates of Jensen and Hermite-Hadamard inequalities for h-Godunova-Levin stochastic processes

Afzal, Waqar; Botmart, Thongchai

doi:10.3934/math.2023366

Cited by 8 publications

(2 citation statements)

References 31 publications

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“…Fractional calculus provides a way to extend the classical calculus to non-integer orders, and has been used to develop new inequalities and bounds for various mathematical objects, such as functions, integrals, and differential equations. The study of fractional calculus and its applications in inequality theory has led to new insights and results in many areas of mathe-matics and physics [19,20]. In conclusion, the study of inequality theory is an important and active area of research in mathematics and other fields.…”

Section: Introductionmentioning

confidence: 99%

Caputo Fractional Derivative Inequalities for Refined Modified ( h , m ) -Convex Functions

Ajmal,

Rafaqat,

Ahmad

2024

Util. Math.

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This paper introduces a novel type of convex function known as the refined modified (h,m)-convex function, which is a generalization of the traditional (h,m)-convex function. We establish Hadamard-type inequalities for this new definition by utilizing the Caputo k-fractional derivative. Specifically, we derive two integral identities that involve the nth order derivatives of given functions and use them to prove the estimation of Hadamard-type inequalities for the Caputo k-fractional derivatives of refined modified (h,m)-convex functions. The results obtained in this research demonstrate the versatility of the refined modified (h,m)-convex function and the usefulness of Caputo k-fractional derivatives in establishing important inequalities. Our work contributes to the existing body of knowledge on convex functions and offers insights into the applications of fractional calculus in mathematical analysis. The research findings have the potential to pave the way for future studies in the area of convex functions and fractional calculus, as well as in other areas of mathematical research.

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Section: Introductionmentioning

confidence: 99%

Caputo Fractional Derivative Inequalities for Refined Modified ( h , m ) -Convex Functions

Ajmal,

Rafaqat,

Ahmad

2024

Util. Math.

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“…For some recent developments related to developed inequalities; see Refs. [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Hermite–Hadamard-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Godunova–Levin and (h1, h2)-Convex Functions

Afzal,

Abbas,

Hamali

et al. 2023

Fractal Fract

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This note generalizes several existing results related to Hermite–Hadamard inequality using h-Godunova–Levin and (h1,h2)-convex functions using a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. This study uses a non-singular kernel and constructs some new theorems associated with fractional order integrals. Furthermore, we demonstrate that the obtained results are a generalization of the existing ones. To demonstrate the correctness of these results, we developed a few interesting non-trivial examples. Finally, we discuss some applications of our findings associated with special means.

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Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for h-Convex Stochastic Process via Interval-Valued Functions

et al. 2023

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Mathematical programming and optimization problems related to fluid dynamics are heavily influenced by stochastic processes associated with integral and variational inequalities. Furthermore, symmetry and convexity are intrinsically related. Over the last few years, both have become increasingly interconnected so that we can learn from one and apply it to the other. The objective of this note is to convert ordinary stochastic processes into interval stochastic processes due to the wide range of applications in various disciplines. We have developed Hermite–Hadamard (H.H), Ostrowski-, and Jensen-type inequalities using interval h-convex stochastic processes. Our main results can be applied to a variety of new and well-known outcomes as specific situations. The results of this study are expected to stimulate future research on inequalities using fractional and fuzzy integral operators. Furthermore, we validate our main findings by providing some non-trivial examples. To demonstrate their general properties, we illustrate the connections between the examined results and those that have already been published. The results discussed in this article can be seen as improvements and refinements to results that have already been published. This is a fascinating subject that can be investigated in the future to identify equivalent inequalities for various convexity types.

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Some novel estimates of Jensen and Hermite-Hadamard inequalities for h-Godunova-Levin stochastic processes

Cited by 8 publications

References 31 publications

Caputo Fractional Derivative Inequalities for Refined Modified ( h , m ) -Convex Functions

Caputo Fractional Derivative Inequalities for Refined Modified ( h , m ) -Convex Functions

Hermite–Hadamard-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Godunova–Levin and (h1, h2)-Convex Functions

Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for h-Convex Stochastic Process via Interval-Valued Functions

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