A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

doi:10.1016/S0252-9602(12)60067-8

Abstract

Abstract:

Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation: f(kx + y) + f(kx − y) = kf(x + y) + kf(x −y) + 2f(kx) − 2kf(x) in Banach modules over a unital Banach algebra.

Key words: Banach module, stability, additive function, cubic function, unital Banach algebra, generalized metric space, fixed-point, JMRassias (or JMR) mixed product-sum of powers of norms

CLC Number:

39B72

XU Tian-Zhou, Rassias John Michael, XU Wan-Xin. A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES[J].Acta mathematica scientia,Series B, 2012, 32(3): 866-892.

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