Iterative schemes for approximating solution of nonlinear operators in Banach spaces

Fixexd point theory and applications

Preedaporn Kanjanasamranwong²  Siwaporn Saewan²  Poom Kumam³  Yeol Je Cho⁴ 

[1] Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, Korea;Department of Mathematics and Statistics, Faculty of Science, Thaksin University, Phatthalung, Thailand;Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangmod, Thrungkru, Thailand

关键词: generalized f-projection operators;    system of generalized Ky Fan’s inequalities;    totally quasi-ϕ-asymptotically nonexpansive mapping;    variational inequalities;    maximal monotone operators;   

DOI  :  10.1186/1687-1812-2013-199

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to present a new modified Halpern-Mann type iterative scheme by using the generalized f-projection operator for finding a common element in the set of zeroes of a system of maximal monotone operators, the set of fixed points of a totally quasi-ϕ-asymptotically nonexpansive mapping and the set of solutions of a system of generalized Ky Fan’s inequalities in a uniformly smooth and strictly convex Banach space with the Kadec-Klee property. Furthermore, we show that our proposed iterative scheme converges strongly to a common element of the sets mentioned above. MSC:47H05, 47H09, 47H10.

【 授权许可】

CC BY