Bi-additive σ-random operator inequalities and random quasi-∗-multipliers on MB-algebras

In this article, the authors prove some bi-additive σ -random operators inequalities and apply these inequalities, together with the fixed-point technique, to get an approximation of the additive σ -random operators in Menger–Banach (MB) spaces. An approximation of random quasi- ∗ -multipliers on MB- ∗ -algebras, associated with the bi-additive σ -random operator inequalities, is also considered.