Two Kinds of Convergences in Hyperbolic Spaces in Three-step Iterative Schemes
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we introduce a new three-step iterative scheme for three finite families of nonexpansive mappings in hyperbolic spaces. And, we establish a strong convergence and a Δ-convergence of a given iterative scheme to a common fixed point for three finite families of nonexpansive mappings in hyperbolic spaces. Our results generalize and unify the several main results of [1, 4, 5, 9]
Abstract
In this paper, we introduce a new three-step iterative scheme for three finite families of nonexpansive mappings in hyperbolic spaces. And, we establish a strong convergence and a Δ-convergence of a given iterative scheme to a common fixed point for three finite families of nonexpansive mappings in hyperbolic spaces. Our results generalize and unify the several main results of [1, 4, 5, 9]
참고문헌 (10)
- Sezgin Akbulut, "Strong and $\Delta $-convergence of a faster iteration process in hyperbolic space", 대한수학회논문집, 30(3), pp.209~219 (2015), 대한수학회
- H.H. Bauschke, "Convex Analysis and Monotone Operator Theory in Hilbert spaces" (2011), Springer-Verlag
- S. Dhompongsa, "On ∆-convergence theorems in CAT(0)-spaces", Com-put. Math. Appl., 56(10), pp.2572~2579 (2008)
- A.R. Khan, "An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces", Fixed Point Theory Appl., 54, pp.12~ (2012)
- S.H. Kim, "Strong convergence and ∆-convergence in CAT(0)-space in three-step iterative schemes with applications", Indian J. Math., 56(1), pp.95~116 (2016)
- U. Kohlenbach, "Some logical metatheorems with applications in functional analysis", Trans. Amer. Math. Soc., 357(1), pp.89~128 (2005)
- L. Leustean, "Nonexpansive iterations in uniformly convex W-hyperbolic spaces. In:Nonlinear Analysis and Optimization I: Nonlinear Analysis", 193~209 (2010)
- S. Reich, "Nonexpansive iterations in hyperbolic spaces", Nonlinear Anal, 15(6), pp.537~558 (1990)
- G.S. Saluja, "Strong and ∆-convergence of new three step iteration process in CAT(0)spaces", Nonlinear Analysis Forum, 20(1), pp.43~52 (2015)
- T. Shimizu, "Fixed points of multivalued mappings in certain convex metric spaces", Topol. Methods Nonlinear Anal., 8(1), pp.197~203 (1996)