scholarly journals New Iterative Manner Involving Sunny Nonexpansive Retractions for Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yaqin Zheng ◽  
Jinwei Shi
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Pseudocontractive Mapping ◽  
Suggested Algorithm ◽  
Pseudocontractive Mappings ◽  
New Iterative Method

Iterative methods for pseudocontractions have been studied by many authors in the literature. In the present paper, we firstly propose a new iterative method involving sunny nonexpansive retractions for pseudocontractions in Banach spaces. Consequently, we show that the suggested algorithm converges strongly to a fixed point of the pseudocontractive mapping which also solves some variational inequality.

scholarly journals A New Iterative Method for Equilibrium Problems and Fixed Point Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Abdul Latif ◽  
Mohammad Eslamian
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Equilibrium Problems ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Common Element ◽  
Continuous Mappings ◽  
New Iterative Method

Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012), Cianciaruso et al. (2010), and many others.

scholarly journals A New Iterative Method for Suzuki Mappings in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Junaid Ahmad ◽  
Kifayat Ullah ◽  
Muhammad Arshad ◽  
Zhenhua Ma
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Weak And Strong Convergence ◽  
Convergence Results ◽  
New Iterative Method

In this paper, an efficient new iterative method for approximating the fixed point of Suzuki mappings is proposed. Some important weak and strong convergence results of the proposed iterative method are established in the setting of Banach space. An example illustrates the theoretical outcome.

scholarly journals An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 61 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonlinear Transformation ◽  
Generalized Variational Inequalities ◽  
Generalized Variational Inequality ◽  
Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

scholarly journals On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Jukkrit Daengsaen ◽  
Anchalee Khemphet
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Convergence Theorem ◽  
Computational Cost ◽  
Closed Intervals ◽  
Iteration Methods ◽  
Nondecreasing Functions ◽  
New Iterative Method

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.

Sign in / Sign up

Export Citation Format

Share Document