An iterative scheme for equilibrium problems and fixed point problems of asymptotically $k$-strict pseudo-contractive mappings
Commun. Korean Math. Soc. 2010 Vol. 25, No. 1, 69-82
https://doi.org/10.4134/CKMS.2010.25.1.69
Printed March 1, 2010
Ziming Wang and Yongfu Su
Tianjin Polytechnic University and Tianjin Polytechnic University
Abstract : In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an asymptotically $k$-strict pseudo-contractive mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results are more general than the known results which are given by many authors. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.
Keywords : iterative scheme, equilibrium problem, asymptotically $k$-strict pseudo-contractive mappings, bifunctions, fixed point
MSC numbers : 47H05, 47H09, 47H10
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