In this paper we established strong and weak convergence theorems for a multi-step iterative scheme with errors for nonself asymptotically nonexpansive mappings in the real uniformly convex Banach space. Our results extend and improve the ones announced by Lin Wang [Lin Wang, Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings, J. Math. A...

In this paper, we study the strong convergence of the Halpern type algorithms for a strongly quasi-nonexpansive sequence of operators. These results extend the results of Saejung [11]. Some applications in infinite family of firmly quasi-nonexpansive mappings, multiparameter proximal point algorithm, constraint minimization and subgradient projection are presented.

In this paper, we consider the convergence of three-step fixed point iterative processes for multivalued nonexpansive mapping with errors, under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the multivalued nonexpansive mapping. Our results extend and improve some recent results.

We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Ban...

In this paper, we proposed a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two total asymptotically nonexpansive non-self mappings and establish some weak convergence theorems for mentioned scheme and mappings in the setting of uniformly convex Banach spaces. Our results extend and generalize several results from the current existing li...

Ab8tmctWe examine the representation of signals by the Wavelet 'lhansform Modulus Maxima together with the alternating projection reconstruction algorithm proposed by Mallat. We show that the projection algorithm of Mallat is not minimum distance and not necessarily nonexpansive. Convergence is therefore not guaranteed. We describe an alternative projection operator which is minimum distance an...

Using the concept of CATp(0) spaces proposed by Khamsi et al. [Khamsi, M. A. and Shukri, S. A., Generalized CAT(0) spaces. Bull. Belg. Math. Soc. Simon Stevin, 24 (2017), No. 3, 417–426], we establish ∆-convergence strong convergence a perturbed variant Agarwal S-iteration process for nonexpansive mapping. Finally, from them deduce results valid α-nonexpansive mappings.

We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly nonexpansive mappings is nearly equal to the average of the ranges of the mappings. A striking application of this result yields that the average of asymptotically r...

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings andmonotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inversestrongly monotone mappings, whic...

The purpose of this paper is to study weak and strong convergence of a new implicit iteration process to a common fixed point for a finite family of nonexpansive mappings in a uniformly convex Banach space. The results obtained in this paper extend and improve the corresponding results of [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of none...