scholarly journals Convergence Rate of Implicit Iteration Process and a Data Dependence Result

2018 ◽  
Vol 11 (1) ◽  
pp. 189
Author(s):  
Isa Yildirim ◽  
Mujahid Abbas
Keyword(s):  
Convergence Rate ◽  
Rate Of Convergence ◽  
Iteration Process ◽  
Data Dependence ◽  
Hyperbolic Spaces ◽  
Type Mapping ◽  
Contractive Type ◽  
Iteration Processes ◽  
Implicit Iteration ◽  
Dependence Result

The aim of this paper is to introduce an implicit S-iteration processand study its convergence in the framework of W-hyperbolic spaces. We showthat the implicit S-iteration process has higher rate of convergence than implicit Mann type iteration and implicit Ishikawa-type iteration processes. We present a numerical example to support the analytic result proved herein. Finally, we prove a data dependence result for a contractive type mapping using implicit S-iteration process.

Some new results of M-iteration process in hyperbolic spaces

2019 ◽  
Vol 35 (2) ◽  
pp. 221-232
Author(s):  
AYNUR SAHIN ◽  
Keyword(s):  
Current Literature ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Data Dependence ◽  
Hyperbolic Spaces ◽  
Convergence Theorems ◽  
Contractive Type

In this paper, we study the M-iteration process in hyperbolic spaces and prove some strong and 4-convergence theorems of this iteration process for generalized nonexpansive mappings. Moreover, we establish the weak w2 - stability and data dependence theorems for a class of contractive-type mappings by using M-iteration process. The results presented here extend and improve some recent results announced in the current literature.

scholarly journals On New Quicker N-Tupled Xed Point Implicit Iterations for Contractive-Like Mappings and Comparison of their Rate of Convergence in Hyperbolic Metric Spaces

2019 ◽  
Author(s):  
Ahmed H. Soliman ◽  
Mohamed A. Barakat ◽  
M. Imdad ◽  
Tamer Nabil
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Rate Of Convergence ◽  
Metric Spaces ◽  
Iteration Process ◽  
Hyperbolic Metric ◽  
Iteration Processes ◽  
Implicit Iteration ◽  
Theoretical Results

In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed point results for nonlinear contractive-like mappings on W-hyperbolic metric spaces. Herein, we demonstrate that our newly implicit iteration schemes have faster rate of convergence than implicit S-iteration process, implicit Ishikawa and Mann type iteration processes. Furthermore, a numerical simulation to improve our theoretical results is obtained.

scholarly journals Convergence and data dependence results of an iteration process in a hyperbolic space

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 569-582 ◽  
Author(s):  
Aynur Şahin ◽  
Metin Başarır
Keyword(s):  
Hyperbolic Space ◽  
Current Literature ◽  
Iteration Process ◽  
Data Dependence ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Appl Math ◽  
Dependence Result

In this paper we prove the strong and 4-convergence theorems of an iteration process of Khan et al. (J. Appl. Math. Comput. 35 (2011) 607-616) for three finite families of total asymptotically nonexpansive nonself mappings in a hyperbolic space. Moreover we obtain the data dependence result of this iteration for contractive-like mappings under some suitable conditions. Also we present some examples to support the results proved herein. Our results extend and improve some recent results announced in the current literature.

scholarly journals Zenali Iteration Method For Approximating Fixed Point of A δZA - Quasi Contractive mappings

2021 ◽  
Vol 34 (4) ◽  
pp. 78-92
Author(s):  
Zena Hussein Maibed ◽  
Ali Qasem Thajil
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Iteration Method ◽  
Iteration Process ◽  
Data Dependence ◽  
Contraction Mappings ◽  
Analytic Proof ◽  
Numerical Example ◽  
Contractive Mappings ◽  
Dependence Result

This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations  like Mann, Ishikawa, oor, D- iterations, and *-  iteration for new contraction mappings called  quasi contraction mappings. And we  proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *-  iteration) equivalent to approximate fixed points of  quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type  by employing zenali iteration also discussed.

Computational Models of Bio Heuristics Based on Physical and Cognitive Processes (Review)

2021 ◽  
Vol 27 (11) ◽  
pp. 563-574
Author(s):  
V. V. Kureychik ◽  
◽  
S. I. Rodzin ◽  
Keyword(s):  
Computational Complexity ◽  
Convergence Rate ◽  
Rate Of Convergence ◽  
Cognitive Processes ◽  
Computational Models ◽  
Optimization Problems ◽  
Search Space ◽  
Experimental Results ◽  
Software Implementation ◽  
Minimum Total Length

Computational models of bio heuristics based on physical and cognitive processes are presented. Data on such characteristics of bio heuristics (including evolutionary and swarm bio heuristics) are compared.) such as the rate of convergence, computational complexity, the required amount of memory, the configuration of the algorithm parameters, the difficulties of software implementation. The balance between the convergence rate of bio heuristics and the diversification of the search space for solutions to optimization problems is estimated. Experimental results are presented for the problem of placing Peco graphs in a lattice with the minimum total length of the graph edges.

scholarly journals Numerical Reckoning Fixed Points of (ρE)-Type Mappings in Modular Vector Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 390 ◽  
Author(s):  
Wissam Kassab ◽  
Teodor Ţurcanu
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Iteration Process ◽  
Existence Results ◽  
Data Dependence ◽  
Vector Spaces ◽  
The Stability ◽  
Recent Version

In this paper, we study an iteration process introduced by Thakur et al. for Suzuki mappings in Banach spaces, in the new context of modular vector spaces. We establish existence results for a more recent version of Suzuki generalized non-expansive mappings. The stability and data dependence of the scheme for ρ -contractions is studied as well.

scholarly journals Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Krzysztof Gdawiec ◽  
Wiesław Kotarski ◽  
Agnieszka Lisowska
Keyword(s):  
Iteration Process ◽  
Higher Order ◽  
Point Of View ◽  
Complex Polynomials ◽  
Root Finding ◽  
Points Of View ◽  
Iteration Processes

A survey of some modifications based on the classic Newton’s and the higher order Newton-like root finding methods for complex polynomials is presented. Instead of the standard Picard’s iteration several different iteration processes, described in the literature, which we call nonstandard ones, are used. Kalantari’s visualizations of root finding process are interesting from at least three points of view: scientific, educational, and artistic. By combining different kinds of iterations, different convergence tests, and different colouring we obtain a great variety of polynomiographs. We also check experimentally that using complex parameters instead of real ones in multiparameter iterations do not destabilize the iteration process. Moreover, we obtain nice looking polynomiographs that are interesting from the artistic point of view. Real parts of the parameters alter symmetry, whereas imaginary ones cause asymmetric twisting of polynomiographs.

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