scholarly journals Data Dependence Result And Stability Of Picard-S Iteration Scheme For Approximating Fixed Point Of Almost Contraction Mappings.

2016 ◽  
Vol 4 (5) ◽  
pp. 760-763
Author(s):  
JAMILZEANA ZAKI ◽  
◽  
ABDULLATEEF-ASSMA KHALDOON. ◽  
Keyword(s):  
Fixed Point ◽  
Iteration Scheme ◽  
Data Dependence ◽  
Almost Contraction ◽  
Contraction Mappings ◽  
Dependence Result

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.

scholarly journals An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Ke Ding ◽  
Jong Kyu Kim ◽  
Qiang Lu ◽  
Bin Du
Keyword(s):  
Fixed Point ◽  
Convergence Rate ◽  
Contraction Mapping ◽  
Nonexpansive Mappings ◽  
Positive Influence ◽  
Iteration Scheme ◽  
Contraction Mappings ◽  
Iterative Schemes ◽  
Comparison Results ◽  
The Given

This paper deals with designing a new iteration scheme associated with a given scheme for contraction mappings. This new scheme has a similar structure to that of the given scheme, in which those two iterative schemes converge to the same fixed point of the given contraction mapping. The positive influence of feedback parameters on the convergence rate of this new scheme is investigated. Moreover, the derived convergence and comparison results can be extended to nonexpansive mappings. As an application, the derived results are utilized to study the synchronization of logistic maps. Two illustrated examples are used to reveal the effectiveness of our results.

scholarly journals Fixed points of Suzuki-type generalized multivalued (f,θ,L)- almost contractions with applications

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 499-518 ◽  
Author(s):  
Naeem Saleem ◽  
Mujahid Abbas ◽  
Basit Ali ◽  
Zahid Raza
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Almost Contraction ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Frame Work ◽  
Proper Generalization

In this paper, we define Suzuki type generalized multivalued almost contraction mappings and prove some related fixed point results. As an application, some coincidence and common fixed point results are obtained. The results proved herein extend the recent results on fixed points of Kikkawa Suzuki type and almost contraction mappings in the frame work of complete metric spaces. We provide examples to show that obtained results are proper generalization of comparable results in the existing literature. Some applications in homotopy, dynamic programming, integral equations and data dependence problems are also presented.

scholarly journals Convergence Analysis for a Modified SP Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Fatma Öztürk Çeliker
Keyword(s):  
Iterative Method ◽  
Convergence Analysis ◽  
Iteration Method ◽  
Data Dependence ◽  
Contraction Mappings ◽  
Dependence Result ◽  
New Iterative Method

We consider a new iterative method due to Kadioglu and Yildirim (2014) for further investigation. We study convergence analysis of this iterative method when applied to class of contraction mappings. Furthermore, we give a data dependence result for fi…xed point of contraction mappings with the help of the new iteration method.

scholarly journals The theory of some asymptotic fixed point theorems

2014 ◽  
Vol 30 (3) ◽  
pp. 361-368
Author(s):  
ANTON S. MURESAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Point Problem ◽  
Shadowing Property ◽  
Contraction Mappings ◽  
Limit Shadowing ◽  
Asymptotic Fixed Point

In this paper we present the theory about some fixed point theorems for convex contraction mappings. We give some results on data dependence of fixed points, on sequences of operators and fixed points, on well-possedness of fixed point problem, on limit shadowing property and on Ulam-Hyers stability for equations of fixed points.

scholarly journals A Picard-S iterative method for approximating fixed point of weak-contraction mappings

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2829-2845 ◽  
Author(s):  
Faik Gürsoy
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Data Dependence ◽  
Weak Contraction ◽  
Dependence Result ◽  
Fredholm Functional

We study the convergence analysis of a Picard-S iterative method for a particular class of weakcontraction mappings and give a data dependence result for fixed points of these mappings. Also, we show that the Picard-S iterative method can be used to approximate the unique solution of mixed type Volterra-Fredholm functional nonlinear integral equation x (t) = F(t, x(t), ?t1,a1... ?tm,am K(t,s,x(s))ds, ?b1,a1...?bm,am H(t,s,x(s))ds). Furthermore, with the help of the Picard-S iterative method, we establish a data dependence result for the solution of integral equation mentioned above.

scholarly journals Fixed point theorems for Presic almost contraction mappings in orbitally complete metric spaces endowed with directed graphs

2016 ◽  
Vol 32 (3) ◽  
pp. 303-313
Author(s):  
PORNPIMON BORIWAN ◽  
◽  
NARIN PETROT ◽  
SUTHEP SUANTAI ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Directed Graphs ◽  
Product Spaces ◽  
Almost Contraction ◽  
Contraction Mappings ◽  
Complete Metric Spaces

The main aim of this paper is to introduce a class of generalized contractions in product spaces in the sense of Presiˇ c. Some examples and fixed point theorems for such introduced mappings in the setting of orbitally ´ complete metric spaces are proved. The results presented here extend and include many existing several results in the literature.

COMMON FIXED POINT THEOREMS FOR CR-ITERATION SCHEME IN THREE MULTIVALUED MAPPINGS

2018 ◽  
Vol 7 (3) ◽  
pp. 51
Author(s):  
KUMAR DAS APURVA ◽  
DHAR DIWAN SHAILESH ◽  
JAIN SWATI ◽  
◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Iteration Scheme ◽  
Multivalued Mappings ◽  
Common Fixed Point Theorems

scholarly journals Multivalued weak cyclic δ-contraction mappings

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pulak Konar ◽  
Samir Kumar Bhandari ◽  
Sumit Chandok ◽  
Aiman Mukheimer
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Cyclic Contraction ◽  
Contraction Mappings ◽  
Multivalued Contraction ◽  
New Type

AbstractIn this paper, we propose some new type of weak cyclic multivalued contraction mappings by generalizing the cyclic contraction using the δ-distance function. Several novel fixed point results are deduced for such class of weak cyclic multivalued mappings in the framework of metric spaces. Also, we construct some examples to validate the usability of the results. Various existing results of the literature are generalized.

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