Translator Disclaimer
Autumn 2017 Stability of the cosine-sine functional equation with involution
Jeongwook Chang, Chang-Kwon Choi, Jongjin Kim, Prasanna K. Sahoo
Adv. Oper. Theory 2(4): 531-546 (Autumn 2017). DOI: 10.22034/aot.1706-1190

Abstract

Let $S$ and $G$ be a commutative semigroup and a commutative group respectively, $\Bbb C$ and $\Bbb R^+$ the sets of complex numbers and nonnegative real numbers respectively, $\sigma : S \to S$ or $\sigma : G \to G$ an involution and $\psi : G \to \Bbb R^+$ be fixed. In this paper, we first investigate general solutions of the equation $$g(x+ \sigma y)=g(x)g(y)+f(x)f(y)$$ for all $ x,y \in S$, where $f, g : S \to \Bbb C$ are unknown functions to be determined. Secondly, we consider the Hyers-Ulam stability of the equation, i.e., we study the functional inequality $$|g(x+\sigma y)-g(x)g(y)-f(x)f(y)|\le \psi(y)$$ for all $x,y \in G$, where $f, g : G \to \Bbb C$.

Citation

Download Citation

Jeongwook Chang. Chang-Kwon Choi. Jongjin Kim. Prasanna K. Sahoo. "Stability of the cosine-sine functional equation with involution." Adv. Oper. Theory 2 (4) 531 - 546, Autumn 2017. https://doi.org/10.22034/aot.1706-1190

Information

Received: 27 June 2017; Accepted: 11 September 2017; Published: Autumn 2017
First available in Project Euclid: 4 December 2017

zbMATH: 1374.39034
MathSciNet: MR3730046
Digital Object Identifier: 10.22034/aot.1706-1190

Subjects:
Primary: 39B82
Secondary: 26D05

Rights: Copyright © 2017 Tusi Mathematical Research Group

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.2 • No. 4 • Autumn 2017
Back to Top