Hybrid algorithms for a family of pseudocontractive mappings

Modified Mann-Halpern Algorithms for Pseudocontractive Mappings

and Applied Analysis 3 We know that T is pseudocontractive if and only if T satisfies the condition 󵄩󵄩󵄩Tx − Ty 󵄩󵄩󵄩 2 ≤ 󵄩󵄩󵄩x − y 󵄩󵄩󵄩 2 + 󵄩󵄩󵄩(I − T)x − (I − T)y 󵄩󵄩󵄩 2 (15) for all x, y ∈ C. Since u ∈ Fix(T), we have from (15) that ‖Tx − u‖ 2 ≤ ‖x − u‖ 2 + ‖x − Tx‖ 2 , (16) for all x ∈ C. By using (13) and (16), we obtain 󵄩󵄩󵄩Tyn − u 󵄩󵄩󵄩 2 ≤ 󵄩󵄩󵄩yn − u 󵄩󵄩󵄩 2 + 󵄩󵄩󵄩yn − Tyn 󵄩󵄩󵄩 2 = 󵄩󵄩󵄩(1 − γn)xn + γnT...

Implicit iteration approximation for a‎ ‎finite family of asymptotically quasi-pseudocontractive type‎ ‎mappings

In this paper‎, ‎strong convergence theorems of Ishikawa type implicit iteration‎ ‎process with errors for a finite family of asymptotically‎ ‎nonexpansive in the intermediate sense and asymptotically‎ ‎quasi-pseudocontractive type mappings in normed linear spaces are‎ ‎established by using a new analytical method‎, ‎which essentially‎ ‎improve and extend some recent results obtained by Yang‎ ‎...

A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings

The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem o...

Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings ✩

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767–77...

Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Pseudocontractive Mappings