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The purpose of this paper is to modify Abbas iteration for two G-nonexpansive mappings. We perform the convergence analysis of newly defined iteration process in uniformly convex Banach space. To compare the rate of convergence of the proposed method with well known Ishikawa iteration, modified S-iteration and Thianwan new iteration processes, a numerical example is also constructed. [ABSTRACT FROM AUTHOR]

We develop versions of the subgradient extragradient method for variational inequalities in Hilbert spaces and establish sufficient conditions for their convergence. First we prove a sufficient condition for a weak convergence of a recent existing algorithm under relaxed assumptions. Then, we propose two other algorithms. Both weak and strong convergence of the considered algorithms are studied. Under additional strong pseudomonotonicity and Lipschitz continuity assumptions, we obtain also a Q -linear convergence rate of these algorithms. Our results improve some recent contributions in the literature. Illustrative numerical experiments are also provided by the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a weak convergence algorithm, called the linesearch algorithm, for solving a split equilibrium problem and nonexpansive mapping (SEPNM) in real Hilbert spaces, in which the first bifunction is pseudomonotone with respect to its solution set, the second bifunction is monotone, and fixed point mappings are nonexpansive. In this algorithm, we combine the extragradient method incorporated with the Armijo linesearch rule for solving equilibrium problems and the Mann method for finding a fixed point of an nonexpansive mapping. We then combine the proposed algorithm with hybrid cutting technique to get a strong convergence algorithm for SEPNM. Special cases of these algorithms are also given. [ABSTRACT FROM AUTHOR]

A new class of contractive mappings called pointwise asymptotically ϕ-strict pseudo-contractions in Hilbert spaces is introduced and weak convergence of the sequence generated by Mann's iterative scheme to a fixed point of a uniformly Lipschitzian and pointwise asymptotically ϕ-strict pseudo-contractive mappingTin a Hilbert space is established. Also, a new kind of monotone hybrid method which is a modification of Mann's iterative scheme for finding a common fixed point of an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ϕ-strict pseudo-contractive mappings is proposed. Strong convergence of the sequence generated by the proposedmonotone hybrid method for an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ϕ-strict pseudo-contractive mappings in a Hilbert space is also shown. The results presented in this article extend and improve some known results in the literature. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a new iterative process for approximating a common fixed point of asymptotically quasi-nonexpansive mappings in a uniformly convex Banach space. Under some appropriate conditions, strong and weak convergence theorems are established for this iterative process. [ABSTRACT FROM AUTHOR]

Abstract: Let be a real uniformly convex Banach space, be a closed convex non-empty subset of which is also a non-expansive retract with retraction . Let be asymptotically non-expansive mappings of into with sequences (respectively), satisfying as , such that . Let be a sequence in for some , for each . Let be a sequence generalized for by Let . Strong and weak convergence of the sequence to a common fixed point of family are proved. [Copyright &y& Elsevier]

We introduce an implicit sequence for an infinite family of nonexpansive mappings in a uniformly convex Banach space. We prove weak and strong convergence theorems for finding a common fixed point of the mappings. Our results not only include Plubtieng et al. (Numer. Funct. Anal. Optim. 2007; 28:737-749), Kikkawa and Takahashi (Ann. Univ. Mariae Curie-Skłodowska Sect. A 2004; 58:69-78), Kimura and Takahashi (Set-Valued Anal. 2008; 16:597-619) as special cases but also are established under the weaker assumptions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for the new two-step iterative scheme in a uniformly convex Banach space. [Copyright &y& Elsevier]

In this paper, a new iterative scheme for approximating common fixed points of two asymptotically nonexpansive nonself-mappings is defined, and weak and strong convergence theorems are established for the new iterative scheme in a uniformly convex Banach space. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the weak and strong convergence of an implicit iteration process to a common fixed point for two finite families of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Xu and Ori, Numer. Funct. Anal. Optim. 2001; 22:767-773, Zhou and Chang, Numer. Fund. Anal. Optim. 2002; 23:911-921, Chidume and Shahzad, Nonlinear. Anal. 2005; 62: 1149-1156. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we are concerned with the study of an iterative scheme with errors involving two nonexpansive mappings. We approximate the common fixed points of these two mappings by weak and strong convergence of the scheme in a uniformly convex Banach space under a condition weaker than compactness. [Copyright &y& Elsevier]