Stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces

Abstract

In this article, we prove the generalized Hyers-Ulam stability of the following Pexider functional inequalitiesin non-Archimedean Banach spaces.

Approximation of Analytic Functions by Solutions of Cauchy-Euler Equation

“…Finally, the Hyers-Ulam stability of the Cauchy-Euler equation (4) was also proven in [16,Theorem 4.5] for the case of ( − 1) 2 − 4 < 0.…”

“…holds for any ∈ (0, ∞), then there exists a solution : (0, ∞) → R of the inhomogeneous Cauchy-Euler equation (4) such that…”

“…We may apply these terminologies for other differential equations. For more detailed definition of the Hyers-Ulam stability and recent papers on this subject, refer to [1][2][3][4]. Obłoza seems to be the first author who investigated the Hyers-Ulam stability of linear differential equations (see [5,6]).…”

Fuzzy Stability of an Aqcq-Functional Equation in Matrix Fuzzy Normed Spaces

“…The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [1,3,24,31,34,35,39,42,44,50,66,57], [60]- [62]). …”

Approximation of Jensen type reciprocal functional equation using fixed point technique

“…Jung [11] investigated the Hyers-Ulam Stability for Jensen equation on a restricted domain and he applied the result to the study of an interesting asymptotic property of additive mappings. The stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces is studied in [13]. Several mathematicians have remarked interesting applications of the Hyers-Ulam-Rassias stability theory to various mathematical problems.…”