A modified Mann iterative scheme by generalized f-projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems

作者：Saewan Siwa****; Kumam Poom^*

来源：Fixed Point Theory and Applications, 2011, 2011(1): 1-21.

DOI：10.1186/1687-1812-2011-104

• The generalized f-projection operator
• relatively quasi-nonexpansive mapping
• B-monotone mappings
• maximal monotone operator
• system of generalized mixed equilibrium problems

The purpose of this paper is to introduce a new hybrid projection method based on modified Mann iterative scheme by the generalized f-projection operator for a countable family of relatively quasi-nonexpansive mappings and the solutions of the system of generalized mixed equilibrium problems. Furthermore, we prove the strong convergence theorem for a countable family of relatively quasi-nonexpansive mappings in a uniformly convex and uniform smooth Banach space. Finally, we also apply our results to the problem of finding zeros of ss-monotone mappings and maximal monotone operators. The results presented in this paper generalize and improve some well-known results in the literature.

• 出版日期2011