90 research outputs found
Approximating fixed point of({\lambda},{\rho})-firmly nonexpansive mappings in modular function spaces
In this paper, we first introduce an iterative process in modular function
spaces and then extend the idea of a {\lambda}-firmly nonexpansive mapping from
Banach spaces to modular function spaces. We call such mappings as
({\lambda},{\rho})-firmly nonexpansive mappings. We incorporate the two ideas
to approximate fixed points of ({\lambda},{\rho})-firmly nonexpansive mappings
using the above mentioned iterative process in modular function spaces. We give
an example to validate our results
Iterative approximation of common attractive points of further generalized hybrid mappings
Our purpose in this paper is (i) to introduce the concept of further
generalized hybrid mappings (ii) to introduce the concept of common attractive
points (CAP) (iii) to write and use Picard-Mann iterative process for two
mappings. We approximate common attractive points of further generalized hybrid
mappings by using iterative process due to Khan SHK generalized to
the case of two mappings in Hilbert spaces without closedness assumption. Our
results are generalizations and improvements of several results in the
literature in different ways.Comment: 12 pages of pdf file created form this tex fil
Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain
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
Approximating Fixed Points by a Two-Step Iterative Algorithm
In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms
Approximating Fixed Points by a Two-Step Iterative Algorithm
In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms
Common fixed points of two quasicontractive operators in normed spaces by iteration, Int
Abstract. We prove a theorem to approximate common fixed points of two quasi-contractive operators on a normed space through an iteration process with errors and more general than the Ishikawa iteration process.Our result generalizes and improves upon, among others, the corresponding result of Berinde Mathematics Subject Classification: 47H10, 54H2
Fixed point results for generalized chatterjea type contractive conditions in partially ordered G-metric spaces
In the framework of ordered G -metric spaces, fixed points of maps that satisfy the generalized Chatterjea type contractive conditions are obtained. The results presented in the paper generalize and extend several well known comparable results in the literature.Scopu
Existence and approximation results for SKC mappings in CAT(0) spaces
Recently, Karap?nar and Tas (Comput. Math. Appl. 61:3370-3380, 2011) extended the class of Suzuki-generalized nonexpansive mappings to the class of SKC mappings. In this paper, we investigate SKC mappings to get a criterion to guarantee a fixed point, via extending the results proved by Karap?nar and Tas into the class of CAT(0) spaces. Further, by using Ishikawa-type iteration scheme for two mappings, we derive approximation fixed point sequence. Our results extend, improve and unify some existing results in this direction, such as (Nonlinear Anal. Hybrid Syst. 4:25-31, 2010) by Nanjaras et al. or (Comput. Math. Appl. 61:109-116, 2011) by Khan and Abbas.Scopu
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