Abstract
Using the fixed point method, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional inequality and of the Cauchy-Jensen additive functional inequality in fuzzy Banach spaces.
Highlights
Introduction and PreliminariesKatsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space
Bag and Samanta 5, following Cheng and Mordeson 6, gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michalek type 7
They established a decomposition theorem of a fuzzy norm into a family of crisp norms and investigated some properties of fuzzy normed spaces 8
Summary
Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. A generalized Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof for mappings f : X → Y , where X is a normed space and Y is a Banach space. 1.7 and proved the generalized Hyers-Ulam stability of the functional inequalities 1.6 and 1.7 in Banach spaces. In 53 , Park et al proved the generalized Hyers-Ulam stability of the functional inequalities 1.6 and 1.7 in fuzzy Banach spaces in the spirit of Hyers, Ulam, and Th. M. Throughout this paper, assume that X is a vector space and that Y, N is a fuzzy Banach space
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