Stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces

Volume 8, Issue 5, pp 776--786 http://dx.doi.org/10.22436/jnsa.008.05.28

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Authors

Sang Og Kim - Department of Mathematics, Hallym University, Chuncheon 200-702, Korea. Abasalt Bodaghi - Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran. Choonkil Park - Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea.

Abstract

In this article, we prove the generalized Hyers-Ulam stability of the following Pexider functional inequalities \[\|f(x) + g(y) + kh(z)\| \leq \| kp (\frac{ x + y}{ k} + z)\|,\] \[\|f(x) + g(y) + h(z)\| \leq \| kp (\frac{ x + y+z}{ k} )\|,\] in non-Archimedean Banach spaces.

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Keywords

• Hyers-Ulam stability
• Pexider Cauchy-Jensen functional inequality
• non-Archimedean space
• additive mapping.

MSC

•  39B05
•  39B52
•  39B62
•  39B82

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