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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)
Publication Information
Journal of applied mathematics & informatics / v.28, no.1_2, 2010 , pp. 233-241 More about this Journal
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
Generalized Hyers-Ulam stability; functional inequality; linear mapping in Banach modules over a $C^*$-algebra;
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