[PDF] Top 20 Strong convergence theorems based on the viscosity approximation method for a countable family of nonexpansive mappings

... A mapping S from C into itself is called nonexpansive if Sx – Sy ≤ x – y, for all x, y ∈ C. Fix(S) := { x ∈ C : Sx = x } is the set of fixed point of S. Note that Fix(S) is closed and convex if S is ... See full document

... -asymptotically nonexpansive nonself mappings and study the strong convergence under a limit condition only in the framework of Banach ...the approximation problem of a solution to a ... See full document

... By using the concept of quasilinearization, we remark that the proof is different from that of Shi and Chen in J. Appl. Math. 2012:421050, 2012. In fact, strong convergence theorems for two given ... See full document

... In this paper, motivated and inspired by the above results, we introduce a new iter- ation scheme in Banach spaces which converges strongly to a common element of the set of fixed points of continuous pseudo-contractive ... See full document

... a family of non- expansive mappings and an accretive operator based on a viscosity iterative ...a viscosity iterative method is discussed. Strong convergence theo- ... See full document

... proved strong convergence theorems for approximation of com- mon element of set of common fixed points of countably infinite family of relatively quasi- nonexpansive ... See full document

... are based on inequality ...a nonexpansive mapping T , Takahashi and Takahashi [] first introduced an iterative scheme by the viscosity approximation ... See full document

... hybrid viscosity approximation method for finding a common fixed point of an infinite family of nonexpansive mappings in ...the strong convergence of this ... See full document

... some strong convergence theorems for fixed points of modified Ishikawa and Halpern iterative processes for a countable family of hemi-relatively nonexpansive mappings in a ... See full document

... The viscosity approximation method (.) is based on the study of Moudafi [], who considered a fixed point problem of a single nonexpansive mapping and proved strong ... See full document

... new viscosity method for hierarchically approximating some common fixed point of an infinite family of nonexpansive mappings and prove the strong convergence theorems ... See full document

... The set of solutions of 5.1 is denoted by EPf. Numerous problems in physics, optimization, and economics are reduced to find a solution of 5.1. Some methods have been proposed to solve the equilibrium problem 11–17. In ... See full document

... extragradient method for fixed point problems and variational inequality problems,” Journal of Inequalities and Applications, ...“Strong convergence theorems for a generalized equilibrium ... See full document

... then u is called a solution of the variational inequality. The set of all solutions of the variational inequality is denoted by VIC, A. It is known that VIC, A is closed and convex. Recently Takahashi and Toyoda 5 ... See full document

... Mosco convergence of their ranges implies their pointwise convergence to the generalized f -projection onto the limit ...a strong convergence theorem for a countable family of α ... See full document

... 5. Yamada, I: The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings. In: Reich, S, Censor, Y, Butnariu D (eds.) ... See full document

... Unfortunately, in recent years, many hybrid algorithms have been very complex, so these complex algorithms are not applicable or are very difficult in applications. Naturally, we hope to obtain some simple and practical ... See full document

... weak convergence theorem for the alternating method with Bregman distances,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, ... See full document

... prove strong convergence of the viscosity approximation method for multivalued nonexpansive mappings in CAT(0) ... See full document

... to nonexpansive non-self-mapping T satisfying Rothe’s boundary condition T(∂C) ⊂ C (here ∂C denotes the boundary of ...a nonexpansive non-self-mapping, and if { x n } is ... See full document