Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces (original) (raw)
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Fixed Point Approximation of Generalized Nonexpansive Mappings in Hyperbolic Spaces
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We prove strong and Δ-convergence theorems for generalized nonexpansive mappings in uniformly convex hyperbolic spaces using S-iteration process due to Agarwal et al. As uniformly convex hyperbolic spaces contain Banach spaces as well as CAT(0) spaces, our results can be viewed as extension and generalization of several well-known results in Banach spaces as well as CAT(0) spaces.
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We introduce a general iterative method for a finite family of generalized asymptotically quasinonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.
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In this paper, we establish strong and D-convergence theorems for a relatively new iteration process generated by generalized nonexpansive mappings in uniformly convex hyperbolic spaces. The theorems presented in this paper generalizes corresponding theorems for uniformly convex normed spaces of Kadioglu and Yildirim (Approximating fixed points of nonexpansive mappings by faster iteration process, arXiv:1402.6530v1 [math.FA], 2014) and CAT(0)-spaces of Abbas et al. (J Inequal Appl 2014:212, 2014) and many others in this direction.
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Fixed Point Results for a Class of Monotone Nonexpansive Type Mappings in Hyperbolic Spaces
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American Journal of Applied Mathematics and Statistics, 2019
In this paper, authors constructed Mann type of iterative method for the finite family of multi valued, nonself and nonexpansive mappings in a uniformly convex hyperbolic space. Authors proved strong convergence theorems of the iterative method, which approximates a common fixed point for the family single valued and multi valued nonexpansive mappings in a complete uniformly convex hyperbolic space which is more general than a complete CAT(0) space and a uniformly convex Banach space. The results in this work extended many results in the literature.
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In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.
Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain
Abstract and Applied Analysis, 2014
We use a three-step iterative process to prove some strong and Δ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.
On Convergence Theorems for Two Generalized Nonexpansive Multivalued Mappings in Hyperbolic Spaces
Thai Journal of Mathematics, 2019
The purpose of this paper is to establish Delta\DeltaDelta-convergence and strong convergence theorems for the mixed Agarwal-O'Regan-Sahu type iterative scheme \cite{3} to approximate a common fixed point for two generalized nonexpansive multivalued mappings in hyperbolic spaces. The results presented in the paper extend and improve some recent results in the literature.