IJPAM: Volume 77, No. 5 (2012)

THE STABILITY OF PEXIDERIZED
CAUCHY FUNCTIONAL EQUATION

Renu Chugh$^1$, Ashish$^2$
$^{1,2}$Department of Mathematics
Maharshi Dayanand University
Rohtak, 124001, INDIA


Abstract. In this paper, we prove the Hyers-Ulam-Rassias stability of the pexiderized Cauchy functional equation $f(x + y + z) - g(x) - h(y) - j(z) = 0$ in Banach spaces. We also use the definition of fuzzy normed spaces to establish the fuzzy version of the Hyers-Ulam-Rassias stability.

Received: September 30, 2011

AMS Subject Classification: 39B72, 39A10, 47H10, 46B03

Key Words and Phrases: pexider equation, fuzzy normed space, fixed point alternative

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 5