Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(1): 181-193

Printed January 31, 2016

https://doi.org/10.4134/BKMS.2016.53.1.181

Copyright © The Korean Mathematical Society.

Certain fractional integral inequalities associated with pathway fractional integral operators

Praveen Agarwal and Junesang Choi

Anand International College of Engineering, Dongguk University

Abstract

During the past two decades or so, fractional integral inequalities have proved to be one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Very recently, many authors have presented some generalized inequalities involving the fractional integral operators. Here, using the pathway fractional integral operator, we give some presumably new and potentially useful fractional integral inequalities whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville type fractional integral operators. Relevant connections of the results presented here with those earlier ones are also pointed out.

Keywords: integral inequalities, Chebyshev functional, Riemann-Liouville fractional integral operator, P\'olya and Szeg\"o type inequalities, pathway fractional integral operator

MSC numbers: Primary 26D10, 26A33; Secondary 26D15

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