Abstract
The present work is about the stability of a Pexiderised quadratic functional equation. The study is in the framework of intuitionistic fuzzy Banach spaces. The approach is through a fixed point method. The stability studied is Hyers-Ulam-Rassias stability type.
Highlights
The study of Hyers-Ulam-Rassias stability for functional equations has a large literature
It has been applied to a number of areas in mathematics like differential equation [18], functional equation [1] isometries [29] etc
In the present context we work with certain functional equations in intuitionistic fuzzy Banach spaces and investigate the Hyers-Ulam-Rassias type stability for
Summary
The study of Hyers-Ulam-Rassias stability for functional equations has a large literature. In the present context we work with certain functional equations in intuitionistic fuzzy Banach spaces and investigate the Hyers-Ulam-Rassias type stability for . The Hyers-Ulam-Rassias stability studies for several types of functional equations on Banach spaces are studied in works like [12, 13, 17, 23]. Intuitionistic fuzzy sets are further extensions of fuzzy sets This has led to a further generalization of fuzzy Banach spaces into the concept of intuitionistic fuzzy Banach spaces which is our choice of the mathematical framework to work upon in the present paper. It is an extension of the ordinary quadratic functional equation These equations have been considered for the purpose of investigating the Hyers-Ulam-Rassias stability in works like [10, 22, 26, 30]. The fixed point result which we apply is obtainable in [4, 9, 28]
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