Iterative schemes for approximating solution of nonlinear operators in Banach spaces
Siwaporn Saewan, Preedaporn Kanjanasamranwong, Poom Kumam, Yeol Je Cho · Fixed Point Theory and Applications · 2013
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.