scholarly journals ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE MAPPINGS

2021 ◽  
pp. 475
Author(s):  
Thierno M. M. Sow
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Optimization Problems ◽  
Common Fixed Points ◽  
Bounded Linear ◽  
Iterative Computation ◽  
Convex Optimization Problems ◽  
Convex Minimization Problems ◽  
Demicontractive Mappings ◽  
New Iterative Method

In this paper, a new iterative method  for solving  convex minimization  problems over the set of common fixed points of quasi-nonexpansive and demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. As an application, we shall utilize our results to solve quadratic optimization  problems involving bounded linear operator. Our theorems are significant improvements on several important recent results.

scholarly journals On Mann’s Method with Viscosity for Nonexpansive and Nonspreading Mappings in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nawab Hussain ◽  
Giuseppe Marino ◽  
Afrah A. N. Abdou
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Common Fixed Points ◽  
Nonspreading Mapping ◽  
Type Mapping ◽  
Nonspreading Mappings

In the setting of Hilbert spaces, inspired by Iemoto and Takahashi (2009), we study a Mann’s method with viscosity to approximate strongly (common) fixed points of a nonexpansive mapping and a nonspreading mapping. A crucial tool in our results is the nonspreading-average type mapping.

scholarly journals Approximations for Equilibrium Problems and Nonexpansive Semigroups

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huan-chun Wu ◽  
Cao-zong Cheng
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Common Fixed Points ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Nonexpansive Semigroup ◽  
New Iterative Method

We introduce a new iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of all common fixed points of a nonexpansive semigroup and prove the strong convergence theorem in Hilbert spaces. Our result extends the recent result of Zegeye and Shahzad (2013). In the last part of the paper, by the way, we point out that there is a slight flaw in the proof of the main result in Shehu's paper (2012) and perfect the proof.

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