Zhang, J., Su, Y., Cheng, Q. (2015). The approximation of common element for maximal monotone operator, generalized mixed equilibrium problem and fixed point problem. test, 23(2), 326-333. doi: 10.1016/j.joems.2014.05.006
Jingling Zhang; Yongfu Su; Qingqing Cheng. "The approximation of common element for maximal monotone operator, generalized mixed equilibrium problem and fixed point problem". test, 23, 2, 2015, 326-333. doi: 10.1016/j.joems.2014.05.006
Zhang, J., Su, Y., Cheng, Q. (2015). 'The approximation of common element for maximal monotone operator, generalized mixed equilibrium problem and fixed point problem', test, 23(2), pp. 326-333. doi: 10.1016/j.joems.2014.05.006
Zhang, J., Su, Y., Cheng, Q. The approximation of common element for maximal monotone operator, generalized mixed equilibrium problem and fixed point problem. test, 2015; 23(2): 326-333. doi: 10.1016/j.joems.2014.05.006

The approximation of common element for maximal monotone operator, generalized mixed equilibrium problem and fixed point problem

Journal of the Egyptian Mathematical Society
Volume 23, Issue 2, 2015, Pages 326-333    PDF (507.34 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2014.05.006
Authors
Jingling Zhang; Yongfu Su* ; Qingqing Cheng
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, PR China
Abstract
The purpose of this paper is to get strong convergence theorems for a countable family of
relatively quasi-nonexpansive mappings fSng
1
n¼0, a maximal monotone operator T, and a generalized mixed equilibrium problem in a uniformly smooth and uniformly convex Banach space lacking
condition UARC. Two examples are given to support our results. One is a countable family of
uniformly closed relatively quasi-nonexpansive mappings but not a countable family of relatively
nonexpansive mappings. Another is uniformly closed but not satisfies condition UARC. Many
recent results in this field have been unified and improved.
Keywords
Relatively quasi-nonexpansive mapping; Generalized f-projection; Uniformly closed; Strong convergence
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