Attractive points and convergence theorems for normally generalized hybrid mappings in CAT(0) spaces

Abstract

We prove -convergence theorems of Mann type to the set of attractive points of normally generalized hybrid mappings in CAT(0) spaces. Consequently, our main result can be applied to the result of Takahashi, Wong and Yao (Journal of Nonlinear and Convex Analysis 15:1087-1103, 2014, Theorem 5.1). MSC: 47H09; 47H10; 54H25

Iterative approximation of attractive points of further generalized hybrid mappings in Hadamard spaces

“…The results presented in this paper modify, extend and improve the corresponding results of Takahashi et al [3] and Kaewkhao et al [4], and others. The main aim of this paper is to prove the demiclosed principle for further generalized hybrid mapping and the -convergence of the sequence generated by the S-iteration process for finding attractive points of such mappings in Hadamard spaces satisfying the (S) property and the (Q 4 ) condition.…”

“…Anyway, since (Q 4 ) implies (Q 4 ), there are some Hadamard spaces that do not satisfy such a condition. The following results were obtained by Kaewkhao et al [4]. Lemma 3.11 Let X be an Hadamard space satisfying the (Q 4 ) condition.…”

“…In 2015, Kaewkhao et al [4] extended the results of Takahashi et al [3] from Hilbert spaces to Hadamard spaces.…”

“…[4]) Consider H = {(x, y) ∈ R 2 : y 2x 2 = 1 and y > 0}. Let d be a metric defined by the function d : H × H → R that assigns to each pair of vectors u = (u 1 , u 2 ) and…”

Attractive points of further 2-generalized hybrid mappings in a complete CAT(0) space

“…and established some of its properties. In 2015, Kaewkhao, Inthakon and Kunwai [10] proved the ∆convergence of a Mann-type scheme to a point in the set of attractive points of normally generalized hybrid mappings. Recently, Cuntavepanit and Phuengrattana [5] studied the class of further generalized hybrid mappings [22] in Hadamard spaces.…”