[PDF] Top 20 Fixed Points in Functional Inequalities

... The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach ... See full document

... This phenomenon is called generalized Ulam-Hyers stability and has been extensively investigated for different functional equations. Almost all proofs used the idea conceived by Hyers. Namely, the additive function ... See full document

... The functional equation fx y f x − y 2fx 2f y is called a quadratic functional ...quadratic functional equation is said to be a quadratic ...quadratic functional equation was proved by Skof 20 ... See full document

... An hierarchical circularly iterative method is introduced for solving a system of variational circularly inequalities with set of fixed points of strongly quasi-nonexpansive mapping problems in this ... See full document

... of fixed points of continuous pseudo-contractive mappings which more general than nonexpansive mappings and the solution set of the variational inequality problem of continuous monotone map- pings which ... See full document

... variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings,” Nonlinear Analysis: Theory, Methods & Applications, ... See full document

... mapping T of H into itself is called nonexpansive if ||Tx - Ty|| ≤ ||x - y|| for all x, y Î H. The set of all fixed points of T is denoted by F(T), that is, F(T) = {x Î C : x = Tx}. A self-mapping f : H ® H ... See full document

... 2. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 3. Aoki, T: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, ... See full document

... common fixed points for commuting ...common fixed points for commuting mappings in more general ...common fixed points in all these concepts is an active area of ...of ... See full document

... The problem is to find some fixed point in C t>0 FixT t. For this, so many algorithms have been developed and under some restrictions partial answers have been obtained 6–11. Assume that F : X → X is a strongly ... See full document

... This problem was introduced by Stampacchia (see []) in . Related to EP and VIP, fixed point problems (FP) of a nonexpansive mapping are also considered by many authors. Recall that a mapping S is nonexpansive if Sx – ... See full document

... [13] H. Piri, Strong convergence for a minimiza- tion problem on solutions of systems of equi- librium problems and common fixed points of an infinite family and semigroup of nonexpan- sive mappings, ... See full document

... fixed points of continuous pseudo-contractive mappings more general than nonexpansive mappings and a solution set of the variational inequality problem for continuous monotone mappings more general than α-inverse ... See full document

... several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem see ... See full document

... the fixed point method see 24, 25, 38, 53–55, we prove the generalized Hyers- Ulam stability of A-quadratic mappings in Banach A-modules associated with the functional equation ...of functional ... See full document

... More recently, Kumam and Katchang 6, W. Kumam and P. Kumam 7, Li and Su 8 and many others see, e.g. 9–12 and the references contained in them studied the problem of fixed point approximations and solutions of some ... See full document

... variational inequalities (1.2) if and only if it is a fixed point of the nonexpansive mapping P F(T ) S, where P F (T ) stands for the metric projection on the closed convex set F ... See full document

... of functional equations for the proof of new fixed point theorems with ...the fixed point method, the stability problems of several functional equations have been extensively investigated by a ... See full document

... 2 I. Yamada, “The hybrid steepest descent method for the variational inequality problem over the in- tersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and ... See full document

... variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems, Non- linear Functional Analysis and its Applications, Part 2 (Berkeley, ... See full document