Approximation of the mixed additive and cubic functional equation in paranormed spaces

Volume 10, Issue 5, pp 2633--2641 http://dx.doi.org/10.22436/jnsa.010.05.29

Publication Date: May 25, 2017 Submission Date: January 21, 2017

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Authors

Zhihua Wang - School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P. R. China. Prasanna K. Sahoo - Department of Mathematics, University of Louisville, Louisville, KY 40292, USA.

Abstract

In this paper, we prove some theorems about the Hyers-Ulam stability of the functional equation \[f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 2[f(2x) - 2f(x)]\] in paranormed spaces. From these theorems, as corollaries, we obtain the stability of the above functional equation with weaker conditions controlled by product of powers of norms and mixed-type product-sum of powers of norms.

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Keywords

• Additive map
• cubic map
• Hyers-Ulam stability
• paranormed space.

MSC

•  39B82
•  39B72
•  35A17
•  47H10

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