A Fixed Point Approach to the Fuzzy Stability of an Additive-Quadratic-Cubic Functional Equation

A Fixed Point Approach to the Fuzzy Stability of an Additive-Quadratic-Cubic Functional Equation

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, 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 Michálek type 7 . T...

A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Functional Equation

The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ Theorem was generalized by Aoki 3 for additive mappings and by Th. M. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. ...

A fixed point approach to the stability of additive-quadratic-quartic functional equations

In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.

A Fixed Point Approach to the Stability of the Cauchy Additive and Quadratic Type Functional Equation

A Fixed Point Approach to the Stability of a Mixed Type Additive and Quadratic Functional Equation

In this paper, we investigate the stability problems for a functional equation f(ax + y) + af(x − y) − a2+3a 2 f(x) −a(a−1) 2 f(−x)− f(y) − af(−y) = 0 by using the fixed point method. Mathematics Subject Classification: Primary 39B82, 39B62; Secondary 47H10