[PDF] Top 20 A Fixed Point Approach to the Stability of a Volterra Integral Equation

... We now introduce one of the fundamental results of fixed point theory. For the proof, we refer to [11]. This theorem will play an important role in proving our main theorems. Theorem 1.1. Let (X ,d) be a ... 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 stability problems of functional equations have been extensively investigated by several math- ematicians ...Hyers–Ulam stability for the linear Volterra integral equation of second ... 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 functional ... See full document

... Therefore, g satisfies (77). Now, we claim that the functional equation (12) is not stable for r = 1 in Corollaries 2.8 and 2.11. Suppose, on the contrary, that there exist a additive mapping A : C → C and a ... 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

... 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

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

... 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

... and fixed point theory. We established the Hyers-Ulam stability of the functional equation (1) in various normed spaces by using fixed point ... See full document

... functional equation must be close to an exact solution of the equation?” The first stability problem concerning group homomorphisms was raised by Ulam 1 in 1940 and affirmatively answered by Hyers in ... See full document

... Therefore, f satisfies (3.14). Now, we claim that the functional Equation (1.2) is not stable for r = 1 in Corollary 3.2. Suppose on the contrary that there exist an additive function A : ℂ ® ℂ and a constant d ... See full document

... Note that the only substantial difference of the generalized metric from the metric is that the range of generalized metric includes the infinity. We now introduce one of fundamental results of fixed point ... See full document

... Hyers-Ulam stability to a number of functional equations and mappings see ...functional equation is a functional equation of the following ... See full document

... functional equation must be close to an exact solution of the equation? ” ...the equation is stable. 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

... equality fx y − fx − f y ≤ ε, for all x and y, can be approximated by an exact so- lution, say an additive function. Later, the result of Hyers was significantly generalized for additive mappings by Aoki 3 see also 4 and ... See full document

... the stability of the Cauchy functional equation: a fixed point approach,” in Iteration Theory (ECIT ’02), ...Hyers-Ulam-Rassias stability theorem for a quartic functional ... See full document

... the stability of the linear functional ...the stability of the linear transformation in Banach ...the stability of the linear mapping in Banach ...Hyers-Ulam-Rassias stability of nonlinear ... See full document

... 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 whole inner ... See full document