scholarly journals Fixed point approximation for S K C $SKC$ -mappings in hyperbolic spaces

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Jong Kyu Kim ◽  
Samir Dashputre
Keyword(s):  
Fixed Point ◽  
Hyperbolic Spaces ◽  
Point Approximation

scholarly journals Fixed Point Approximation of Generalized Nonexpansive Mappings in Hyperbolic Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Jong Kyu Kim ◽  
Ramesh Prasad Pathak ◽  
Samir Dashputre ◽  
Shailesh Dhar Diwan ◽  
Rajlaxmi Gupta
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Point Approximation

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.

scholarly journals Fixed Point Approximation of Monotone Nonexpansive Mappings in Hyperbolic Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Amna Kalsoom ◽  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Tareq M. Al-Shami ◽  
Amna Bibi ◽  
...  
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Hyperbolic Space ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Point Approximation ◽  
Convergence Results ◽  
Iteration Processes

Fixed points of monotone α -nonexpansive and generalized β -nonexpansive mappings have been approximated in Banach space. Our purpose is to approximate the fixed points for the above mappings in hyperbolic space. We prove the existence and convergence results using some iteration processes.

scholarly journals Fixed Point Approximation for Asymptotically Nonexpansive Type Mappings in Uniformly Convex Hyperbolic Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Shin Min Kang ◽  
Samir Dashputre ◽  
Bhuwan Lal Malagar ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Point Approximation ◽  
Convergence Results ◽  
Asymptotically Nonexpansive

We use a modifiedS-iterative process to prove some strong andΔ-convergence results for asymptotically nonexpansive type mappings in uniformly convex hyperbolic spaces, which includes Banach spaces and CAT(0) spaces. Thus, our results can be viewed as extension and generalization of several known results in Banach spaces and CAT(0) spaces (see, e.g., Abbas et al. (2012), Abbas et al. (2013), Bruck et al. (1993), and Xin and Cui (2011)) and improve many results in the literature.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

Implied costs in loss networks

1989 ◽  
Vol 21 (3) ◽  
pp. 661-680 ◽  
Author(s):  
P. J. Hunt
Keyword(s):  
Fixed Point ◽  
Objective Function ◽  
Rate Of Change ◽  
Loss Networks ◽  
Point Approximation ◽  
Asymptotic Accuracy

Implied costs in loss networks are measures of the rate of change of an objective function with respect to the parameters of the network. This paper considers these costs and the costs predicted by the Erlang fixed-point approximation. We derive exact expressions for the implied costs and consider the asymptotic accuracy of the approximation. We show that the approximation is asymptotically valid in some cases but is not valid in one important limiting regime. We also show that a linearity approximation for the implied costs is asymptotically correct when taken over suitable subsets of links.

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