scholarly journals A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space

2011 ◽  
Vol 2011 (1) ◽  
Author(s):  
De-ning Qu ◽  
Cao-zong Cheng
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Fixed Point Problems ◽  
Strong Convergence Theorem ◽  
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.

scholarly journals Solving split generalized mixed equality equilibrium problems and split equality fixed point problems for nonexpansive-type maps

2020 ◽  
Vol 36 (1) ◽  
pp. 119-126
Author(s):  
M. O. NNAKWE
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Real Banach Space ◽  
Equilibrium Problems ◽  
Fixed Point Problems ◽  
Strong Convergence Theorem ◽  
Uniformly Convex ◽  
Type Condition ◽  
Common Solution ◽  
Uniformly Smooth

"Let X be a 2-uniformly convex and uniformly smooth real Banach space. In this paper, an iterative algorithmofKrasnosel’skii-typeis constructed and used to approximate a common solution ofsplit generalized mixed equalityequilibrium problems(SGMEEP)andsplit equality fixed point problems(SEFPP)forquasi-ψ-nonexpansive maps.A strong convergence theorem of the sequence generated by this algorithm is proved without imposing anycompactness-type condition on either the operators or the space considered. The theorem proved improves andcomplements important recent results in the literature. "

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