Convergence to common fixed points of averaged mappings without commutativity assumption in Hilbert spaces

2007 ◽  
Vol 67 (6) ◽  
pp. 1758-1763 ◽  
Author(s):  
Yonghong Yao ◽  
Rudong Chen
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Common Fixed Points ◽  
Averaged Mappings

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 On the viscosity rule for common fixed points of two nonexpansive mappings in Hilbert spaces

2017 ◽  
Vol 1 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Sayed Fakhar Abbas Naqvi ◽  
◽  
Muhammad Saqib Khan ◽  
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points

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.

Iterative algorithms for split common fixed points of demicontractive operators without priori knowledge of operator norms

2018 ◽  
Vol 34 (3) ◽  
pp. 459-466
Author(s):  
YONGHONG YAO ◽  
◽  
JEN-CHIH YAO ◽  
YEONG-CHENG LIOU ◽  
MIHAI POSTOLACHE ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Convergence Result ◽  
Common Fixed Points ◽  
Operator Norms ◽  
Priori Knowledge

The split common fixed points problem for demicontractive operators has been studied in Hilbert spaces. An iterative algorithm is considered and the weak convergence result is given under some mild assumptions.

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