Iterative schemes for approximating solution of nonlinear operators in Banach spaces

作者：Saewan Siwa****^*; Kanjanasamranwong Preeda****; Kumam Poom; Cho Yeol Je

来源：Fixed Point Theory and Applications, 2013, 2013(1): 199.

DOI：10.1186/1687-1812-2013-199

• generalized f-projection operators
• system of generalized Ky Fan%26apos
• s inequalities
• totally quasi-phi-asymptotically nonexpansive mapping
• variational inequalities
• maximal monotone operators

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-phi-asymptotically nonexpansive mapping and the set of solutions of a system of generalized Ky Fan%26apos;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.

• 出版日期2013