Best approximation of $(\mathcal{G}_{1},\mathcal{G}_{2})$-random operator inequality in matrix Menger Banach algebras with application of stochastic Mittag-Leffler and $\mathbb{H}$-Fox control functions

Abstract

AbstractWe stabilize pseudostochastic $(\mathcal{G}_{1},\mathcal{G}_{2})$ ( G 1 , G 2 ) -random operator inequality using a class of stochastic matrix control functions in matrix Menger Banach algebras. We get an approximation for stochastic $(\mathcal{G}_{1},\mathcal{G}_{2})$ ( G 1 , G 2 ) -random operator inequality by means of both direct and fixed point methods. As an application, we apply both stochastic Mittag-Leffler and $\mathbb{H}$ H -fox control functions to get a better approximation in a random operator inequality.