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

Abstract

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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Acknowledgements

The authors are thankful to the anonymous referees and the area editor for giving valuable comments and suggestions which helped to improve the final version of this paper.

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Correspondence to Reza Saadati.

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Srivastava, H.M., Saadati, R. & Jang, S.Y. Bi-additive \(\sigma\)-random operator inequalities and random quasi-\(*\)-multipliers on MB-algebras. Math Sci (2021). https://doi.org/10.1007/s40096-020-00368-z

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Keywords

  • Random quasi-multiplier on \(MC^*\)-algebra
  • Random quasi-\(*\)-multiplier on MB-algebra
  • Fixed-point technique
  • Bi-additive \(\sigma\)-random operator inequality

Mathematics Subject Classification

  • Primary 54H12
  • 46L05
  • 47H10, Secondary 39B62
  • 43A22