Let E be a real Banach space, {Ti}i=1 be a finite family of continuous pseudocontractive self mappings of E and G : E → E be a mapping which is both δ -strongly accretive and λ -strictly pseudocontractive of Browder-Petryshyn type such that δ + λ 1 . We propose a new implicit iteration scheme with perturbed mapping G for the approximation of common fixed points of {Ti}i=1 . For an arbitrary ini...

A extension of Nakajo and Takahashi’s modification of Mann’s iterative process to the Ishikawa iterative process is given. The strong convergence of a modified Ishikawa iterative scheme to a common fixed point of a finite family of Lipschitz pseudocontractive self-mappings on a closed convex subset of a Hilbert space is proved. Our theorem extends several known results. c © 2007 Elsevier Ltd. A...

*Correspondence: [email protected] 2Basic Experimental & Teaching Center, Henan University, Kaifeng, 475000, China Full list of author information is available at the end of the article Abstract In this article, a mean iterative algorithm is investigated for finding a common element in the solution set of generalized equilibrium problems and in the fixed point set of strictly pseudocontractive ma...

We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of fixed point of infinitely many strict pseudocontractive mappings and the set of solutions of an equilibrium problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. Our results improve and extend the corresponding res...

In this article, we introduce a hybrid iteration involving inertial-term for split equilibrium problem and fixed point finite family of asymptotically strictly pseudocontractive mappings. We prove that the sequence converges strongly to solution common The results proved extend improve recent Chang et al. [S. S. Chang, H. W. J. Lee, C. K. Chan, L. Wang, Qin, Appl. Math. Comput., \(\bf 219\) (20...

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...

LetK be a closed convex subset of a real Banach space E, T : K → K is continuous pseudocontractive mapping, and f : K → K is a fixed L-Lipschitzian strongly pseudocontractive mapping. For any t ∈ (0,1), let xt be the unique fixed point of t f + (1− t)T . We prove that if T has a fixed point and E has uniformly Gâteaux differentiable norm, such that every nonempty closed bounded convex subset of...

This paper is concerned with a common element of the set of common fixed points for two infinite families of strictly pseudocontractive mappings and the set of solutions of a system of cocoercive quasivariational inclusions problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a novel general iterative scheme based on the viscosity approximation method...