Hermite-Hadamard, Trapezoid and Midpoint Type Inequalities Involving Generalized Fractional Integrals for Convex Functions

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Kara H., Erden S., Budak H.

SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, vol.20, no.2, pp.85-107, 2023 (ESCI)

• Publication Type: Article / Article
• Volume: 20 Issue: 2
• Publication Date: 2023
• Doi Number: 10.22130/scma.2022.552775.1102
• Journal Name: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
• Page Numbers: pp.85-107
• Kocaeli University Affiliated: No

Abstract

We first construct new Hermite-Hadamard type in-equalities which include generalized fractional integrals for convex functions by using an operator which generates some significant fractional integrals such as Riemann-Liouville fractional and the Hadamard fractional integrals. Afterwards, Trapezoid and Mid-point type results involving generalized fractional integrals for func-tions whose the derivatives in modulus and their certain powers are convex are established. We also recapture the previous results in the particular situations of the inequalities which are given in the earlier works.