Bi-additive $$\sigma$$-random operator inequalities and random quasi-$$*$$-multipliers on MB-algebras

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

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