NEW TRAPEZIUM INEQUALITIES FOR GENERALIZED INTEGRAL OPERATORS PERTAINING m-CONVEX FUNCTIONS AND THEIR APPLICATIONS

Authors

DOI:

https://doi.org/10.37560/matbil219005d

Keywords:

Hermite-Hadamard inequality, Hölder's inequality, power mean inequality, \(m\)-convex, general fractional integrals

Abstract

The author discovered an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite-Hadamard type integral inequalities for differentiable functions that are in absolute value at certain powers \(m\)-convex. 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 the field of integral inequalities.

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Published

2019-01-01

Issue

Vol. 43 No. 2 (2019): 43 (LXIX) 2 (2019)

Section

Articles

License

Copyright (c) 2019 Matematichki Bilten

Creative Commons License

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

How to Cite

[1]
A. Kashuri, “NEW TRAPEZIUM INEQUALITIES FOR GENERALIZED INTEGRAL OPERATORS PERTAINING m-CONVEX FUNCTIONS AND THEIR APPLICATIONS”, Mat. Bilt., vol. 43, no. 2, pp. 31–52, Jan. 2019, doi: 10.37560/matbil219005d.