[PDF] Top 20 Stability of a Mixed Type Functional Equation on Multi-Banach Spaces: A Fixed Point Approach

... the stability problems of several functional equations and approximate homomorphisms have been extensively investigated by a number of authors, and there are many interesting results concerning this ... See full document

... In the last section, we prove the stability problem in the sense of Hyers-Ulam-Rassias for the functional equations 1.1 and 1.2 on Multi-Banach spaces by using fixed point approach.. We [r] ... See full document

... metric spaces. Since then, the theory of probabilistic metric spaces has been developed by many authors in many directions; see [6], [7] and the references ...metric spaces appears to be interested ... See full document

... to point out the direct method for studying the stability of func- tional ...the fixed point alternative method to solve the Ulam ...the fixed point alternative method to solve ... See full document

... of stability problems for functional equations is related to a question of Ulam [1] concerning the stability of group homomorphisms and affirmatively answered for Banach spaces by Hyers ... See full document

... an equation is called a quadratic functional ...vector spaces is quadratic if and only if there exists a unique symmetric bi- additive function B such that f (x) = B(x, x) for all x (see ...quadratic ... See full document

... The stability problem of functional equations originated from the following question of Ulam [18]: Under what condition does there exist an additive mapping near an approximately additive mapping? In 1941, ... See full document

... Euler-Lagrange type additive ...Hyers-Ulam stability of the functional equation (1.1) in Banach modules over a C ∗ ...Hyers-Ulam stability of the functional ... See full document

... the stability of the linear transformation in Banach spaces, ...Ulam-Hyers stability of a 2-variable AC-mixed type functional equation: direct and fixed ... See full document

... the stability of the additive mapping as a special ...Hyers-Ulam stability for the linear mapping between Banach spaces was ...Hyers-Ulam stability of the additive mapping was proved by ... See full document

... Hyers stability by replacing the bound θ (||x|| p ||y|| q ) in [9], by a mixed one involving the product and sum of powers of norms, that is, θ {||x|| p ||y|| p + (||x|| 2p + ||y|| 2p ... See full document

... of multi-normed space is introduced by Dales and Polyakov ...operator spaces and Banach lattices. Motivations for the study of multi-normed spaces and many examples are given in ...the ... See full document

... The functional equation f(x + y) + f(x - y) = 2f(x) + 2f(y) is called a quadratic func- tional ...quadratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem ... See full document

... The stability problem of functional equations originated from a question of Ulam [1] concerning the stability of group ...Hyers-Ulam stability of func- tional ... See full document

... Over the last seven decades, the above problem was tackled by numerous authors and its solutions via various forms of functional equations including mixed type additive and cubic functional ... See full document

... Hyers-Ulam stability of the additive-quadratic-quartic functional equation ...fuzzy Banach spaces for an odd ...Hyers-Ulam stability of the additive- quadratic-quartic ... See full document

... in Banach spaces, which is also a quadratic and equivalent to ...Hyers-Ulam stability of ...the functional equation ...and equation (0.2) in complex Banach spaces ... See full document

... f (x + y) + f (x − y) = 2f(x) + 2f (y) (1.1) is related to a symmetric bi-additive function [30, 31]. It is natural that this equa- tion is called a quadratic functional equation. In particular, every ... See full document

... f (x + y) + f(x − y) = 2f(x) + 2f (y) (1.1) is related to a symmetric bi-additive function (cf. [1, 16]). It is natural that (1.1) is called a quadratic functional equation. In particular, every solution of ... See full document

... The stability of mixed type functional equations have been extensively investigated by a number of math- ematicians in referenes (see [3–5, 14–22, 28–31, 33–38, 43, 48, ...the fixed ... See full document