IJPAM: Volume 112, No. 1 (2017)

Title

HYERS-ULAM STABILITY OF QUADRATIC FUNCTIONAL
EQUATIONS ON DIVISIBLE SQUARE-SYMMETRIC
GROUPOID

Authors

Gwang Hui Kim$^1$, Hwan-Yong Shin$^2$
$^1$Department of Mathematics
Kangnam Universaty
Yongin, Gyeonggi, 16979, REPUBLIC OF KOREA
$^2$Department of Mathematics
Chungnam National University
99 Daehangno, Yuseong-gu, Daejeon, 34134, REPUBLIC OF KOREA

Abstract

Let $ (X, \diamond)$ be a divisible square-symmetric groupoid, and $ (Y, \ast, d) $ a complete metric divisible square-symmetric groupoid. In this paper, we obtain the Hyers-Ulam stability problem of functional inequality $ d(f(x \diamond y)\ast f(x \diamond y^{-1}), \sigma_{\ast}(f(x)\ast f(y))) \leq \varepsilon (x,y)$ for approximate mapping $f: X \rightarrow Y$ of functional equation $ h(x\diamond y) \ast h(x \diamond y^{-1}) = \sigma_{\ast}( h(x)\ast h(y) ) $ differing by $ \varepsilon : X^2 \rightarrow [0, \infty )$.

History

Received: September 28, 2016
Revised: October 16, 2016
Published: January 26, 2017

AMS Classification, Key Words

AMS Subject Classification: 39B52, 39B72, 47H09
Key Words and Phrases: Hyers-Ulam stability, quadratic functional equation, square-symmetric groupoid, fixed point theorem

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How to Cite?

DOI: 10.12732/ijpam.v112i1.15 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 112
Issue: 1
Pages: 189 - 201


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