Positive-additive Nearly functional equation in C*-algebras by two approaches
H. Azadi Kenary
Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75914-353, Iran.
Pages 80-88 | Received 20 March 2025, Accepted 17 July 2025, Published 19 July 2026
Abstract
In this paper, we introduce the following positive-additive functional equation in C^*-algebras
f\left(x+3x^\frac{2}{3} \sqrt[3]{y}+3y^\frac{2}{3} \sqrt[3]{x}+y\right) = f(x)+3f(x)^\frac{2}{3} \sqrt[3]{f(y)}+3f(y)^\frac{2}{3} \sqrt[3]{f(x)}+f(y).
Using fixed point methods, we prove the stability of the positive-additive functional equation in C^*-algebras. Moreover, we prove the Hyers-Ulam stability of the positive-additive functional equation in C^*-algebras by the direct method of Hyers and Ulam.
Keywords: Hyers-Ulam stability, C^*-algebra, fixed point, positive-additive functional equation.
MSC numbers: 46L05, 47H10, 39B52.
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