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Fractional versions of Hadamard inequalities for strongly $(s,m)$-convex functions via Caputo fractional derivatives

Laxmi Rathour|Lakshmi Narayan Mishra|Vishnu Narayan Mishra|Ghulam Farid|Sidra Bibi
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2023.03|한국수학논문집 (Korean Journal of Mathematics)|제31권 제1호|pp. 75-94

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키워드

Hadamard inequalityConvex functionStrongly convex functionCaputo fractional derivatives
주제분류수학

초록

We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly $(s,m)$-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.

Abstract

We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly $(s,m)$-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.

참고문헌 (25)

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