Approximation of general Pexider functional inequalities in fuzzy Banach spaces

Volume 12, Issue 4, pp 206--216 http://dx.doi.org/10.22436/jnsa.012.04.02

Publication Date: December 05, 2018 Submission Date: April 02, 2018 Revision Date: August 05, 2018 Accteptance Date: October 26, 2018

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Authors

Gang Lu - Department of Mathematics, School of Science, ShenYang University of Technology, Shenyang 110870, P. R. China. Jincheng Xin - Department of Mathematics, School of Science, ShenYang University of Technology, Shenyang 110870, P. R. China. Yuanfeng Jin - Department of Mathematics, Yanbian University, Yanji 133001, People's Republic of China. Choonkil Park - Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea.

Abstract

In this paper, we investigate a fuzzy version of a generalized Hyers-Ulam-Rassias type stability for the following Pexider functional inequalities \[ f(x+y)+f(x-y)+g(z)+h(l) \leq kp\left(\frac{2x+z+l}{k}\right) , \] \[ f(x+y)+f(x-y) + g(z)+k h(l) \leq kp\left(\frac{ x+ z }{k}+l\right) , \] where $k$ are nonzero real scalars. In the fuzzy normed linear space setting is presented. In this condition, we give an alternative proof of this result in fuzzy Banach space.

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Keywords

• Fuzzy approximation
• Pexider functional inequality
• fuzzy Banach space

MSC

•  39B62
•  39B52
•  46B25

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