[PDF] Top 20 A Fixed Point Approach to the Stability of Pexider Quadratic Functional Equation with Involution

... 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 prove the Hyers-Ulam-Rassias stability of the functional equation ...Hyers-Ulam-Rassias stability approach for the proof of new fixed ... See full document

... 13. Nikodem, K: On quadratic set-valued functions. Publ Math Debrecen. 30, 297 – 301 (1984) 14. Nikodem, K: On Jensen ’ s functional equation for set-valued functions. Radovi Mat. 3, 23 – 33 (1987) ... 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

... a quadratic functional equation. Quadratic functional equations were used to characterize inner product spaces ...the quadratic equation ...is quadratic if and only ... 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 Aoki see ... See full document

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

... of functional equations araised as follows: When is it true that a function, which approximately satisfies a functional equation, must be close to an exact solution of the equation? If the ... 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

... Under what condition is there a homomorphism near an approximately homomorphism between a group and a metric group? This is called the stability problem of functional equations which was first raised by S. ... See full document

... The aim of this section is to give an alternative proof for that result in 15, Section 3, based on the fixed point method. Also, our method even provides a better estimation. Theorem 3.1. Let X be a linear ... See full document

... in which ⊥ is an abstract orthogonality relation was first investigated by Gudder and Strawther [8]. They defined ⊥ by a system consisting of five axioms and described the general semi-continuous real-valued solution of ... See full document

... The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group ...Hyers-Ulam stability or as Hyers-Ulam-Rassias stability of ... See full document

... Hyers’ theorem was generalized by Aoki 15 for additive mappings and by Th. M. Rassias 16 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. M. Rassias 16 has provided a lot of influence in ... 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

... the quadratic equation ...is quadratic if and only if there exists a unique symmetric biadditive mapping B such that f x Bx, x for all x see 16, 21, 26, ... See full document

... an involution of the normed space E and k is a fixed positive ...Hyers-Ulam-Rassias stability of the func- tional equation. The Hyers-Ulam stability on unbounded domains is also ... See full document