Convergence theorems for three finite families of multivalued nonexpansive mappings

Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces

In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditi...

Strong Convergence Theorems for a Finite Family of Nonexpansive Mappings

Let H be a real Hilbert space, C a nonempty closed convex subset of H , and T : C → C a mapping. Recall that T is nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is called a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T , that is, F(T) = {x ∈ C : Tx = x}. Recall that a self-mapping f : C → C is a contraction on C, if there exists a constant α∈ (0...

Convergece Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings

Let E be a real Banach space, K a closed convex nonempty subset of E, and T1,T2, . . . ,Tm : K → K asymptotically quasi-nonexpansive mappings with sequences (resp.) {kin}n=1 satisfying kin → 1 as n → ∞, and ∑∞ n=1(kin − 1) < ∞, i = 1,2, . . . ,m. Let {αn}n=1 be a sequence in [ , 1− ], ∈ (0,1). Define a sequence {xn} by x1 ∈ K , xn+1 = (1− αn)xn + αnT n 1 yn+m−2, yn+m−2 = (1− αn)xn + αnT 2 yn+m−...

Convergence Theorems for -Nonexpansive Mappings in CAT(0) Spaces

In this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete CAT(0) space for SP-iterative process and Thianwan's iterative process.

Convergence Theorems For Two Finite Families of Uniformly L-Lipschitzian Mappings