Certain weighted Young and Polya-Szego-type inequalities involving Marichev-Saigo-Maeda fractional integral operators with applications

Abstract

In this paper, we establishes certain new weighted Young and Polya-Szego-type inequalities involving Marichev-Saigo-Maeda fractional integral operators. Meanwhile, corresponding weighted Cauchy-Schwarz type inequalities, Shisha-Mond type inequalities and  Diaz-Metcalf type inequalities for Marichev-Saigo-Maeda fractional integral operators are also obtained. As applications, some estimates for weighted Chebyshev-type inequalities with two unknown functions for Marichev-Saigo-Maeda fractional integral operators are presented. The main results of this paper are more general and include a great number of existing classical inequalities.