TRAPEZIUM-TYPE INEQUALITIES VIA GENERALIZED INTEGRAL OPERATORS FOR STRONGLY CONVEX FUNCTIONS AND THEIR APPLICATIONS

Authors

DOI:

https://doi.org/10.37560/matbil22461007l

Keywords:

Hermite-Hadamard inequality, Hölder inequality, power mean inequality, strongly \(m\)-convex function, general fractional integrals, special means, error estimation

Abstract

The aim of this paper is to introduce an identity for a generalized integral operator via differentiable function. By using this integral equation, some new bounds on Hermite-Hadamard type integral inequalities for differentiable functions are derived that are in absolute value at certain powers strongly convex with positive modulus \(c\). By taking suitable choices of function, some interesting results are obtained. At the end, some applications of presented results to special means and new error estimates for the trapezium formula have been analyzed. The ideas and techniques of this paper may stimulate further research in different areas of pure and applied sciences.

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Published

2022-05-14

Issue

Vol. 46 No. 1 (2022): 46 (LXXII) 1 (2022)

Section

Articles

License

Copyright (c) 2022 Matematichki Bilten

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
R. Liko, A. Kashuri, M. A. Ali, H. Budak, and M. Abbas, “TRAPEZIUM-TYPE INEQUALITIES VIA GENERALIZED INTEGRAL OPERATORS FOR STRONGLY CONVEX FUNCTIONS AND THEIR APPLICATIONS”, Mat. Bilt., vol. 46, no. 1, pp. 7–24, May 2022, doi: 10.37560/matbil22461007l.