A CONVERGENCE THEOREM FOR COMMON ELEMENTS OF EQUILIBRIUM PROBLEMS AND MAPPINGS SATISFYING CONDITION (Φ-Eµ) IN UNIFORMLY CONVEX AND UNIFORMLY SMOOTH BANACH SPACES
2018 ◽
Vol 1
(30)
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pp. 67-77
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In this paper, we propose a new hybrid iteration for finding a common element of solution set of equilibrium problems and the fixed point set of mappings satisfying condi- tion (Φ-Eµ), and establish the convergence of this iteration in uniformly convex and uniformly smooth Banach spaces. From this theorem, we geta corollary for the convergence for equilibrium problems and mappings satisfying condition (Eµ) in real Hilbert spaces. In addition, an example is provided to illustrate for the convergence of equilibrium problems and mappings satisfying condition (Φ-Eµ). These results are the generations and improvements of some existing results in the literature
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1991 ◽
Vol 157
(1)
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pp. 189-210
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2011 ◽
Vol 15
(3)
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pp. 1007-1020
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Keyword(s):