The classical Mazur–Ulam theorem which states that every sur-jective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly convex normed spaces.

‎In 1897‎, ‎Hensel introduced a normed space which does‎ ‎not have the Archimedean property‎. ‎During the last three decades‎ ‎theory of non--Archimedean spaces has gained the interest of‎ ‎physicists for their research in particular in problems coming‎ ‎from quantum physics‎, ‎p--adic strings and superstrings‎. ‎In this paper‎, ‎we prove‎ ‎the generalized Hyers--Ulam--Rassias stability for a‎ ...

In this paper, the nonlinear stability of a functional equation in the setting of non-Archimedean normed spaces is proved. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the and the theory of functional equations are also presented Key word: Hyers Ulam Rassias stability • cubic mappings • generalized normed space • Banach spac...

In this paper, we give a general solution of a refined quadratic functional equation and then investigate its generalized Hyers–Ulam stability in quasi-normed spaces and in non-Archimedean normed spaces. AMS Subject Classification: 39B82, 39B62

We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea of t-norm and t-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framewor...

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of nonArchimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-...

the goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--archimedean spacesand also in $p$--banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

The goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--Archimedean spacesand also in $p$--Banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

In this paper, we investigate the Hyers-Ulam stability for the system of additive, quadratic, cubicand quartic functional equations with constants coecients in the sense of dectic mappings in non-Archimedean normed spaces.

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.