Strong Convergence for Hybrid ImplicitS-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings

Strong Convergence of CQ Iteration for Asymptotically Nonexpansive Mappings

Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

Convergence Analysis of an Iteration Scheme for Lipschitz Strongly Pseudocontractive Mappings

CONVERGENCE ANALYSIS OF AN ITERATION SCHEME FOR LIPSCHITZ STRONGLY PSEUDOCONTRACTIVE MAPPINGS Shin Min Kang Department of Mathematics, Gyeongsang National University, Jinju 660-701, KOREA [email protected] Arif Rafiq Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan [email protected] ABSTRACT In this paper, we establish the strong convergence for the Agarwal et al. [1] ite...

Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings

and Applied Analysis 3 Very recently, Qin et al. 16 proposed the composite Halpern type iterative scheme in a uniformly smooth Banach space as follows: x0 x, u ∈ C, zn γnxn ( 1 − γn ) Txn, yn βnxn ( 1 − βn ) Tzn, xn 1 αnu 1 − αn yn, n ≥ 0, 1.6 and showed strong convergence of the sequence {xn} generated by 1.6 under the following control conditions: i ∑∞ n 0αn ∞; ii limn→∞αn 0, limn→∞βn 0 and 0...

Strong Convergence of a Modified Halpern’s Iteration for Nonexpansive Mappings

A mapping T : C → C is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. We denote by Fix T {x ∈ C : Tx x} the set of fixed points of T . In the last ten years, many papers have been written on the approximation of fixed point for nonlinear mappings by using some iterative processes see, e.g., 1–18 . An explicit iterative process was initially introduced, in 1967, by Halpern 3 i...

Strong Convergence for Hybrid S-Iteration Scheme