scholarly journals Construction techniques of projection sets in hybrid methods for infinite weakly relatively nonexpansive mappings with applications

2019 ◽  
Vol 2019 (1) ◽  
Keyword(s):  
Hybrid Methods ◽  
Nonexpansive Mappings ◽  
Relatively Nonexpansive Mappings ◽  
Construction Techniques ◽  
Relatively Nonexpansive

scholarly journals Strong Convergence Theorems for Families of Weak Relatively Nonexpansive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
Yekini Shehu
Keyword(s):  
Strong Convergence ◽  
Convergence Theorem ◽  
Real Banach Space ◽  
Hybrid Methods ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Relatively Nonexpansive Mappings ◽  
Uniformly Smooth ◽  
Relatively Nonexpansive

We construct a new Halpern type iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space using the properties of generalizedf-projection operator. Using this result, we discuss strong convergence theorem concerning generalH-monotone mappings. Our results extend many known recent results in the literature.

scholarly journals A Strong Convergence Theorem for Relatively Nonexpansive Mappings and Equilibrium Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Mei Yuan ◽  
Xi Li ◽  
Xue-song Li ◽  
John J. Liu
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Projection Method ◽  
Convergence Theorem ◽  
Projection Operator ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

Relatively nonexpansive mappings and equilibrium problems are considered based on a shrinking projection method. Using properties of the generalizedf-projection operator, a strong convergence theorem for relatively nonexpansive mappings and equilibrium problems is proved in Banach spaces under some suitable conditions.

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