[PDF] Top 20 Projection algorithms for treating asymptotically quasi ϕ nonexpansive mappings in the intermediate sense

... iterative algorithms, the oldest and simplest one is the Picard iterative ...general nonexpansive mappings, the Picard iterative algo- rithm fails to converge to fixed points of nonexpansive ... See full document

... cally quasi-nonexpansive mappings with respect to Bregman distances in the intermedi- ate sense by using the shrinking projection ...of mappings of nonexpansive type with ... See full document

... The aim of this paper is to present an iterative method for solving solutions of a fam- ily of mixed equilibrium problems with a relaxed η-α-monotone mapping and a nonlin- ear operator equation involving an infinite ... See full document

... In this paper, common solutions to an equilibrium problem and a nonlinear operator equation involving a finite family of asymptotically quasi- φ -nonexpansive mappings in the ... See full document

... iterative algorithms, the oldest and simplest one is the Picard iterative ...general nonexpansive mappings, the Picard iterative algorithm fails to converge to fixed points of nonexpansive ... See full document

... The purposes of this article is to study Algorithms (1.1) and (1.2) with the help of additional metric projections for the new mapping. The organization of this article is as follows. In Section 2, we provide some ... See full document

... relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach ...relatively nonexpansive mapping from C into itself and let { α n } be a sequence of real numbers such that  ≤ α ... See full document

... of quasi-φ-nonexpansive mappings and the class of asymptotically quasi-φ -nonexpansive mappings are generalizations of the class of quasi-nonexpansive ... See full document

... Lemma . [] Let E be a reflexive, strictly convex, and smooth Banach space such that both E and E ∗ have the Kadec-Klee property. Let C be a nonempty closed and convex subset of E. Let T : C → C be a closed ... See full document

... In this paper, we modify Halpern and Mann’s iterations for finding a fixed point of an infinite family of quasi- φ -asymptotically nonexpansive mappings in the intermediate sense in ... See full document

... Notice that J is weakly sequentially continuous. Letting k → ∞ , we find that z – p, Jp – Jz ≥ . It follows from the monotonicity of J that z – p, Jp – Jz ≤ . Since the space is uniformly convex, we find that z = p. This ... See full document

... some restrictions. Further, using this result, they also investigated the case that B = ∂f , where f : H → (–∞, ∞] is a proper lower semicontinuous convex function. Convergence theorems are established in the framework ... See full document

... We also remark that the viscosity approximation method was first introduced by Moudafi [] in the framework of Hilbert spaces. Moudafi proved that the desired so- lution is not only a fixed point of nonlinear ... See full document

... imal point algorithm; for more detail, see [] and the references therein. Regularization methods recently have been investigated for treating zero points of monotone operators; for [–] and the references ... See full document

... Nonlinear analysis plays an important role in optimization problems, economics and transportation. The theory of variational inequalities has emerged as a rapidly growing area of research because of its applications; see ... See full document

... total quasi-φ -asymptotically nonexpansive mapping with non- negative real sequences ν n and μ n with ν n → , μ n →  as n → ∞ and a strictly ... See full document

... for quasi-nonexpansive and asymptotically quasi-nonex- pansive mappings in Banach spaces, by using Theorem 13, we prove some convergence theorems of the modified Ishikawa iterative ... See full document

... metric projection is nonexpansive only in a Hilbert ...generalized projection map C : E → C in a Banach space which is an analogue of the metric projection in a Hilbert ... See full document

... the projection algorithm for treating solutions of the equilibrium problem and fixed points of generalized asymptoti- cally quasi-φ-nonexpansive ... See full document

... In this paper, motivated and inspired by the results mentioned above, we prove strong and weak convergence theorems for finding a common element of the set of fixed point of a quasi- φ -asymptotically ... See full document