Ishikawa iterative algorithms for a generalized equilibrium problem and fixed point problems of a pseudo-contraction mapping

2009 ◽  
Vol 46 (3) ◽  
pp. 331-345 ◽  
Author(s):  
Jian-Wen Peng ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Contraction Mapping ◽  
Iterative Algorithms ◽  
Fixed Point Problems ◽  
Generalized Equilibrium Problem ◽  
Generalized Equilibrium

scholarly journals Approximation of common solutions for a fixed point problem of asymptotically nonexpansive mapping and a generalized equilibrium problem in Hilbert space

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Richard Osward ◽  
Santosh Kumar ◽  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Equilibrium Problem ◽  
Fixed Point Problem ◽  
Asymptotically Nonexpansive Mapping ◽  
Point Problem ◽  
Generalized Equilibrium Problem ◽  
Common Solution ◽  
Asymptotically Nonexpansive ◽  
Generalized Equilibrium

Abstract In this paper, we introduce an iterative algorithm to approximate a common solution of a generalized equilibrium problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequences generated by the iterative algorithm converge strongly to a common solution of the generalized equilibrium problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. Some applications of main results are also provided.

scholarly journals Algorithms of common solutions for a fixed point of hemicontractive-type mapping and a generalized equilibrium problem

2017 ◽  
Vol 5 (1) ◽  
pp. 20
Author(s):  
Habtu Zegeye ◽  
Tesfalem Hadush Meche ◽  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Research Area ◽  
Common Element ◽  
Generalized Equilibrium Problem ◽  
Type Mapping ◽  
Generalized Equilibrium

In this paper, we introduce and study an iterative algorithm for finding a common element of the set of fixed points of a Lipschitz hemicontractive-type multi-valued mapping and the set of solutions of a generalized equilibrium problem in the framework of Hilbert spaces. Our results improve and extend most of the results that have been proved previously by many authors in this research area.

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