Habtu Zegeye

Convergence Theorems for Non-Self Mappings in CAT(0) Spaces

ABSTRACT In this paper, we prove strong convergence of Mann iterative schemes to fixed points of multi-valued demicontractive non-self mappings in complete CAT(0) spaces under appropriate conditions. In addition, △− convergence or strong convergence of Mann iterative scheme to a fixed point of single-valued k-strictly pseudocontractive non-self mapping is obtained. Our theorems improve and unify most of the results in the literature.

Approximating solutions of Hammerstein type equations in Banach spaces

Abstract Let X be a real Banach space and X∗ be its dual. Let F: X → X∗ and K: X∗ → X be Lipschitz monotone mappings. In this paper an explicit iterative scheme is constructed for approximating solutions of the Hammerstein type equation, 0 = u + KF u, when they exist. Strong convergence of the scheme is obtained under appropriate conditions. Our results improve and unify many of the results in the literature.