Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A CAUCHY-JENSEN FUNCTIONAL INEQUALITY IN BANACH MODULES OVER A $C^*$-ALGEBRA

  • Najati, Abbas (Department of Mathematics, University of Mohaghegh Ardabili)
  • Published : 2010.01.30
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Abstract

In this paper, we investigate the following functional inequality $${\parallel}f(\frac{x\;+\;y}{2}\;+\;z)\;+\;f(\frac{x\;+\;y}{2}\;+\;y)\;+\;f(\frac{y\;+\;z}{2}\;+\;x){\parallel\;\leq\;\parallel}2f(x\;+\;y\;+\;z)\parallel$$ in Banach modules over a $C^*$-algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a $C^*$-algebra.

Keywords

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