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Hermite-Hadamard’s mid-point type inequalities for generalized fractional integrals

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas volume 114, Article number: 73 (2020) Cite this article

Abstract

Some Hermite-Hadamard’s mid-point type inequalities related to Katugampola fractional integrals are obtained where the first derivative of considered mappings is Lipschitzian or convex. Also some mid-point type inequalities are given for Lipschitzian mappings, with the aim of generalizing the results presented in previous works. Finally, some generalized inequalities in connection with special means are provided.

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Acknowledgements

The authors would like to thank the reviewer for his/her valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P. O. Box 1339, Bojnord, 94531, Iran

    M. Rostamian Delavar

  2. Mathematics, College of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC, 8001, Australia

    S. S. Dragomir

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  1. M. Rostamian Delavar
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  2. S. S. Dragomir
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Correspondence to M. Rostamian Delavar.

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Delavar, M.R., Dragomir, S.S. Hermite-Hadamard’s mid-point type inequalities for generalized fractional integrals. RACSAM 114, 73 (2020). https://doi.org/10.1007/s13398-020-00795-6

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  • DOI: https://doi.org/10.1007/s13398-020-00795-6

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