scholarly journals Strong convergence theorem for the modified generalized equilibrium problem and fixed point problem of strictly pseudo-contractive mappings

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Sarawut Suwannaut ◽  
Atid Kangtunyakarn
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Convergence Theorem ◽  
Fixed Point Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Generalized Equilibrium Problem ◽  
Contractive Mappings ◽  
Generalized Equilibrium

scholarly journals Iterative approximations with hybrid techniques for fixed points and equilibrium problems

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1997-2009
Author(s):  
Afrah Abdou ◽  
Badriah Alamri ◽  
Yeol Cho ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Hybrid Techniques ◽  
Contractive Mappings ◽  
Generalized Equilibrium

In this paper, we consider an iterative algorithm by using the shrinking projection method for solving the fixed point problem of the pseudo-contractive mappings and the generalized equilibrium problems. We prove some lemmas for our main result and a strong convergence theorem for the proposed algorithm.

A Strong Convergence Theorem for Solving the Split Equality Fixed Point Problem

2021 ◽  
pp. 2140014
Author(s):  
Xueling Zhou ◽  
Meixia Li ◽  
Haitao Che
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Prior Information ◽  
Fixed Point Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Contractive Mappings ◽  
Adaptive Stepsize ◽  
Operator Norms

In this paper, we study the split equality fixed point problem and propose a new iterative algorithm with a self-adaptive stepsize that does not need the prior information of the operator norms and is calculated easily. The L-Lipschitz and quasi-pseudo-contractive mappings are chosen as the operators in the algorithm since they have a wider range of applications. Moreover, we prove that the sequence generated by the algorithm strongly converges to the solution of the problem. Finally, we check the feasibility and effectiveness of the algorithm by comparing with other algorithms.

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