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http://dx.doi.org/10.7468/jksmeb.2018.25.2.149

STRONG CONVERGENCE OF HYBRID ITERATIVE SCHEMES WITH ERRORS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS

Kim, Seung-Hyun (Department of Mathematics, Kyungsung University)
Kang, Mee-Kwang (Department of Mathematics, Dongeui University)

Publication Information

The Pure and Applied Mathematics / v.25, no.2, 2018 , pp. 149-160 More about this Journal

Abstract

In this paper, we prove a strong convergence result under an iterative scheme for N finite asymptotically $k_i-strictly$ pseudo-contractive mappings and a firmly nonexpansive mappings $S_r$ . Then, we modify this algorithm to obtain a strong convergence result by hybrid methods. Our results extend and unify the corresponding ones in [1, 2, 3, 8]. In particular, some necessary and sufficient conditions for strong convergence under Algorithm 1.1 are obtained.

Keywords

strong convergence; asymptotically pseudo-contractive mapping; firmly nonexpansive mapping; equilibrium problem; hybrid iterative scheme;

Citations & Related Records

Reference

1	L.C. Ceng, S. Al-Homidan, Q.H. Ansari & J.C. Yao: An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings. J. Comp. Appl. Math. 223 (2009), 967-974. DOI
2	S.H. Kim, M.K. Kang & B.S. Lee: Two-steps hybrid iterative scheme with errors for generalized equilibrium problems and common fixed point problems. Appl. Math. E-Notes 15 (2015), 276-286.
3	P. Kumam, N. Petrot & R. Wangkeeree: A hybrid iterative scheme for equilibrium problems and fixed point problems of asymptotically k-strict pseudo-contractions J. Comp. Appl. Math. 233 (2010), 2013-2026. DOI
4	G. Marino & H.K. Xu: Weak and strong convergence theorems for strict pseudo- contractions in Hilbert space. J. Math. Anal. Appl. 329 (2007), 336-346. DOI
5	C. Martinez-Yanes & H.K. Xu: Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal. 64 (2006), 2400-2411. DOI
6	A. Moudafi & M. Thera: Proximal and dynamical approaches to equilibrium problems. Lecture Notes in Economics and Mathematical Systems, vol. 477, Springer-Verlag, New York, 1999.
7	M.O. Osilike & D.I. Igbokwe: Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations. Comput. Math. Appl. 40 (2000), 559-567. DOI
8	X. Qin, Y.J. Cho, S.M. Kang & M. Shang: A hybrid iterative scheme for asymptotically k-strictly pseudo-contractions in Hilbert spaces. Nonlinear Anal. 281 (2003), 516-524.