[PDF] Top 20 Fuzzy Stability of the Pexiderized Quadratic Functional Equation: A Fixed Point Approach

... the stability of functional equation was first suggested by Hyers 17 while he was trying to answer the question originated from the problem of Ulam 18, and it is called a direct method because it ... See full document

... for all x, y ∈ E, controlled by a product of different powers of norms, where θ ≥ 0 and real numbers p, q, r : p q / 1, and retained the condition of continuity of f tx in t ∈ R for each fixed x ∈ E. Besides he ... See full document

... An inquisitive question that was given a serious thought by S.M. Ulam [45] concerning the stability of group homomorphisms gave rise to the stability problem of functional equations. The laborious ... See full document

... cularly, fuzzy differential equation is a strong topic with large application areas, for example, in population models [10], civil engineering [11] and so ... See full document

... The stability problem concerning the stability of group homomorphisms of functional equations was originally introduced by Ulam [] in ...Ulam stability prob- lem was partially solved by Hyers ... See full document

... Assume that inequality 3.3 is also satisfied with another function G : a, ∞ → C which is a solution of 1.1. As G is a solution of 1.1, G satisfies that Gx Gx 1 − i/ √ x 1Gx ΛGx for all x ≥ a. In other words, G is a ... See full document

... Dhombres, Functional Equations in Several Variables, Cambridge Univ, Press, ...the stability of the linear transformation in Banach spaces, ...Intuitionistic Fuzzy Stability of n-Dimensional ... See full document

... Hyers-Ulam stability of a pexiderized quadratic ...The stability problems of several functional equations have been extensively investigated by a number of authors and there are many ... See full document

... The stability problem of functional equations originated from a question of Ulam 13 concerning the stability of group ...Hyers-Ulam stability or as Hyers- Ulam-Rassias stability of ... See full document

... various functional equations have been investigated by many mathematicians 9, 10. In the following, we first recall some fundamental results in the fixed point theory. Let X be a set. A function d : ... See full document

... Hyers-Ulam-Rassias stability of C ∗ -algebra homomorphisms and of generalized derivations on C ∗ -algebras for the following Cauchy-Jensen functional equation 2fx y/2 z fx fy 2fz, which was ... See full document

... called quadratic functional ...of functional eqaution ...a quadratic mapping. A Hyers-Ulam stability problem for the quadratic functional equation was proved by ... See full document

... of stability theory of functional equations for the proof of new fixed point theorems with applica- ...using fixed point methods, the stability problems of several ... See full document

... a quadratic functional ...tic functional equation is said to be a quadratic ...Hyers-Ulam stability of the quadratic functional equation was proved by Skof ... See full document

... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem for the quadratic functional ... See full document

... the stability of group homomorphisms was proposed by Ulam 1: Under what conditions does there exist a group homomorphism near an approximately group homomorphism? In 1941, Hyers 2 considered the case of ... See full document

... of functional equations is as ...a functional equation must be close to an exact solution of the equation?” The first stability problem concerning group homomorphisms was raised by Ulam ... See full document

... the fixed point method to the investigation of the Cauchy additive functional equation see 16, ...Hyers-Ulam stability of Cauchy and Jensen functional ... See full document

... Cauchy functional equation f(x + y) = f(x) + f(y), 〈 x, y 〉 = ...additivity equation everywhere. Thus, orthogonal Cauchy equation is not equivalent to the classic Cauchy equation on the ... See full document

... A fixed-point approach to the stability of a functional equation on quadratic forms Jae-Hyeong Bae1 and Won-Gil Park2* * Correspondence: [email protected] 2 Department of Mathematics E[r] ... See full document