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 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.

A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

2021 ◽  
pp. 1-21
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
A. Nafea
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Mixed Monotone Property ◽  
Cone Metric Spaces ◽  
System Of Integral Equations ◽  
Tripled Fixed Point ◽  
Fixed Point Techniques ◽  
Theoretical Results ◽  
Cone Metric

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

A Note on "Implicit Mann Fixed Point Iterations for Pseudo-Contractive Mappings"

2011 ◽  
Vol 393-395 ◽  
pp. 543-545
Author(s):  
Hong Jun Li ◽  
Yong Fu Su
Keyword(s):  
Fixed Point ◽  
Convergence Theorem ◽  
Nonempty Subset ◽  
Applied Mathematics ◽  
Iteration Process ◽  
Implicit Iteration Process ◽  
Contractive Mappings ◽  
Contractive Map ◽  
Fixed Point Iterations ◽  
Implicit Iteration

Ljubomir Ciric, Arif Rafiq, Nenad Cakic, Jeong Sheok Umed [ Implicit Mann fixed point iterations for pseudo-contractive mappings, Applied Mathematics Letters 22 (2009) 581-584] introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the relatively convergence theorem. However, the content of mann theorem is fuzzy. In this paper, we will give some comments . Let be a Banach space and be a nonempty subset of . A mapping is called hemi-contractive (see [1]) if and In [1], the authors introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the following convergence theorem.

scholarly journals Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2267
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la De la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Control Function ◽  
Cone Metric Spaces ◽  
Tripled Fixed Point ◽  
Contractive Type ◽  
Theoretical Results ◽  
Cone Metric

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

scholarly journals Multivalued generalizations of fixed point results in fuzzy metric spaces

2016 ◽  
Vol 21 (2) ◽  
pp. 211-22 ◽  
Author(s):  
Tatjana Došenovic ◽  
Dušan Rakic ◽  
Biljana Caric ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Multivalued Mappings ◽  
Altering Distance Function ◽  
Fuzzy Metric ◽  
Altering Distance ◽  
Theoretical Results

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results.

scholarly journals Approximation of Endpoints for α—Reich–Suzuki Nonexpansive Mappings in Hyperbolic Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1692
Author(s):  
Izhar Uddin ◽  
Sajan Aggarwal ◽  
Afrah A. N. Abdou
Keyword(s):  
Fixed Point ◽  
Convergence Analysis ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Metric ◽  
Convergence Theorems ◽  
Hyperbolic Metric Space

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving α—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and Δ—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results.

scholarly journals Fixed point theorems of finite family with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 155-166
Author(s):  
Singh Saluja
Keyword(s):  
Fixed Point ◽  
Recent Result ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Convex Metric Spaces

In this paper, we prove that a multi-step iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converges strongly to a common fixed point of the mappings in convex metric spaces. Our results extend and improve the recent result of Kim et al. [9, 10] and many known results.

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