Strong Convergence of A Hybrid Method for Infinite Family of Nonexpansive Mapping and Variational Inequality

Savita Rathee, Monika Swami

Abstract


The motivation behind this paper is to use hybrid method for searching a typical component of the set of fixed point of an infinite family of non expansive mapping and the set of monotone, Lipschtiz continuous variational inequality problem. The contemplated method is combination of two method one is extragradient method and the other one is DQ method. Also, we demonstrate the strong convergence of the designed iterative technique, under some warm conditions.

Keywords


Non expansive mapping; Fixed point problem; Projection method; Variational inequality problem; extragradient method

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References


Ceng, L. C, Teboulle, M. and Yao, J. C.," Weak convergence of an iterative method for pseudomonotone variational inequalities and fixed point problems", J Optim Theory Appl.146(2010),19-31.

Ceng, L. C., Hadjisavvas, N. and Wong, N. C.." Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems", J. Glob Optim., 46(2010), 635-646.

Goebel, K. and Kirk, W. A.," Topics in Metric Fixed Point Theory", Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 28(1990).

Korpelevich, G. M.," An extragradient method for finding saddle points and other problems", Ekonomikai Matematicheskie Metody, 12(1976), 747-756.

Nadezhkina, N., Takahashi, W.," Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings", SIAM J Optim., 16(2006),1230-1241.

Opial, Z.," Weak convergence of the sequence of successive approximations of nonexpansive mappings. Bull Am MathSoc.73, 595-597(1967).

Qin, X., Cho, Y. J. Kang, J. I. and Kang, S. M.," Strong convergence theorems for an infinte family of non expansive mappings in Banach spaces", J. of Computational and Applied Mathematics, 230(2009), 121-127.

Shimoji, K. and Takahashi, W.," Strong convergence to common fixed points of infinite nonexpasnsive mappings and applications" Taiwan J. Math.,5(2001), 387-404.

Stampacchia, G.," Formes bilinearies coercitives sur les ensembles convexes", D.R. Math. Sci.Paris., 258(1964), 4414-4416.

Yao, Y., Liou, Y. C. and Yao, J. C.," Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings", Fixed Point Theory and Applications, 12 (2007).

Yao, Y., Liou, Y. C., Wong, M. and Yao, J. C.," Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems", Fixed Point Theory and Applications, 1-10(2011).




DOI: https://doi.org/10.22342/jims.27.1.955.90-102

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