Functional inequalities in generalized quasi-Banach spaces

Volume 9, Issue 5, pp 2481--2491 http://dx.doi.org/10.22436/jnsa.009.05.47

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Authors

Ming Fang - School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China. - School of Science, Yanbian University, Yanji 133001, P. R. China. Gang Lu - Shenyang University of Technology, Shenyang 110870, P. R. China. Dong He Pei - School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China.

Abstract

In this paper, we investigate the Hyers-Ulam stability of the following function inequalities \[\|af(x) + bg(y) + ch(z)\| \leq \| K_p (\frac{ ax + by + cz}{k}) \| ;\] \[\|af(x) + bg(y) + Kh(z)\| \leq \| K_p (\frac{ ax + by }{k} + z) \| ;\] in generalized quasi-Banach spaces, where \(a; b; c;K\) are nonzero real numbers.

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Keywords

• Hyers-Ulam stability
• additive functional inequality
• generalized quasi-Banach space
• additive mapping.

MSC

•  47H10
•  54H25

References

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