Refinements of Hermite-Hadamard inequality for operator convex function

Han, Junmin; Shi, Jinjing

doi:10.22436/jnsa.010.11.38

Cited by 6 publications

(1 citation statement)

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“…The Hadamard inequality can also be generalized to functions, where it provides a bound on the product of the values of a convex function over an interval in terms of its integral over that interval. In this context, the inequality is known as the Hadamard-Fischer inequality, and has important applications in probability theory, functional analysis, and optimization [18,19].…”

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%