Abstract
In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field.
Highlights
One of the interesting questions concerning the stability problems of functional equations is as follows: When is it true that a mapping approximately satisfying a functional equation must be close to the solution of the given functional equation? Such an idea was suggested in 1940 by Ulam [1] as follows
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affilfor all x, y ∈ G? If such a mapping exists, does a homomorphism h : G → G exist such that iations
In 1941, Hyers [2] studied nearly additive mappings in Banach spaces that satisfied the very weak Hyers stability defined by a positive constant
Summary
One of the interesting questions concerning the stability problems of functional equations is as follows: When is it true that a mapping approximately satisfying a functional equation must be close to the solution of the given functional equation? Such an idea was suggested in 1940 by Ulam [1] as follows. In 1941, Hyers [2] studied nearly additive mappings in Banach spaces that satisfied the very weak Hyers stability defined by a positive constant. A number of authors have examined and generalized stability problems of various functional equations that have been discussed in different normed spaces by using a fixed-point approach over the last few decades (see [5,6,7,8,9,10,11,12]). Skof [13] demonstrated the stability of quadratic functional equations for mappings between normed space and Banach space. The paper [18] demonstrates the stability of the additive Cauchy equation in non-Archimedean FN-spaces under the strongest t-norm TM.
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