On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals

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Budak H., Bilisik C. C., Sarikaya M. Z.

SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, no.2, pp.65-79, 2022 (ESCI)

• Publication Type: Article / Article
• Publication Date: 2022
• Doi Number: 10.22130/scma.2022.539417.992
• Journal Name: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
• Page Numbers: pp.65-79
• Kocaeli University Affiliated: No

Abstract

In this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of phi(x) = (omega) over bar (kappa(1)kappa(2)/H) is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [34] under the condition phi' (kappa(1) + kappa(2) - H) >= phi' (H) instead of harmonically convexity of (omega) over bar. Moreover, some new inequalities for k-fractional integrals are given as special cases of main results.