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

Abstract

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

Keywords

• Stochastic matrix control function
• Mittag-Leffler
• ( G 1 , G 2 ) $(\mathcal{G}_{1},\mathcal{G}_{2})$ -random operator inequality
• Menger Banach algebra
• H $\mathbb{H}$ -Fox function