scholarly journals Existence and Uniqueness of Fixed Points of Generalized F-Contraction Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
A. P. Farajzadeh ◽  
M. Delfani ◽  
Y. H. Wang
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Admissible Function ◽  
Simulation Function ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Banach Contraction

The newest generalization of the Banach contraction through the notions of the generalized F-contraction, simulation function, and admissible function is introduced. The existence and uniqueness of fixed points for a self-mapping on complete metric spaces by the new constructed contraction are investigated. The results of this article can be viewed as an improvement of the main results given in the references.

scholarly journals On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Areej S. S. Alharbi ◽  
Hamed H. Alsulami ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Admissible Function ◽  
Point Theory ◽  
Contractive Condition ◽  
Simulation Function ◽  
The Given ◽  
Admissible Functions

We investigate the existence and uniqueness of certain operators which form a new contractive condition via the combining of the notions of admissible function and simulation function contained in the context of completeb-metric spaces. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

scholarly journals The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Shih Du ◽  
Erdal Karapınar ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Coincidence Points ◽  
Complete Metric Spaces

The basic motivation of this paper is to extend, generalize, and improve several fundamental results on the existence (and uniqueness) of coincidence points and fixed points for well-known maps in the literature such as Kannan type, Chatterjea type, Mizoguchi-Takahashi type, Berinde-Berinde type, Du type, and other types from the class of self-maps to the class of non-self-maps in the framework of the metric fixed point theory. We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces.

scholarly journals On some fixed point theorems for multivalued F-contractions in partial metric spaces

2021 ◽  
Vol 54 (1) ◽  
pp. 151-161
Author(s):  
Santosh Kumar ◽  
Sholastica Luambano
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Partial Metric Spaces

Abstract Altun et al. explored the existence of fixed points for multivalued F F -contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F F -contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained 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 Generalized α-Meir-Keeler contraction mappings on Branciari b-metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5445-5456 ◽  
Author(s):  
Selma Gülyaz ◽  
Erdal Karapınar ◽  
İnci Erhan
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Contraction Mappings

In this paper, ?-Meir-Keeler and generalized ?-Meir-Keeler contractions on Branciari b-metric spaces are introduced. Existence and uniqueness of fixed points of such contractions are discussed and related theorems are proved. Various consequences of the main results are also presented.

scholarly journals Fixed points results via simulation functions

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2343-2350 ◽  
Author(s):  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Simulation Function ◽  
Complete Metric Spaces ◽  
Admissible Mapping ◽  
Simulation Functions

In this paper, we present some fixed point results in the setting of a complete metric spaces by defining a new contractive condition via admissible mapping imbedded in simulation function. Our results generalize and unify several fixed point theorems in the literature.

scholarly journals Fixed Points of Generalized α -Meir-Keeler Contraction Mappings in S b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Thounaojam Stephen ◽  
Yumnam Rohen ◽  
Naeem Saleem ◽  
Mairembam Bina Devi ◽  
K. Anthony Singh
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Contraction Mappings

In this note, we define Meir-Keeler contraction in S b -metric spaces. Further, by adding the concept of α -admissible mappings, we define generalized α s -Meir-Keeler contraction and used it for examining the existence and uniqueness of fixed points. Various results are also given as a consequence of our results.

scholarly journals Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Projection Operators ◽  
Oblique Projection ◽  
Bounded Operators ◽  
Limit Operators ◽  
Complete Metric Spaces ◽  
Closed Operators ◽  
Banach Contraction

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach’s spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

scholarly journals Best Proximity point for Z-contraction and Suzuki type Z-contraction mappings with an application to fractional calculus

2016 ◽  
Vol 17 (2) ◽  
pp. 185 ◽  
Author(s):  
Somayya Komal ◽  
Poom Kumam ◽  
Dhananjay Gopal
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Functional Differential

In this article, we introduced the best proximity point theorems for $\mathcal{Z}$-contraction and Suzuki type $\mathcal{Z}$-contraction in the setting of complete metric spaces. Also by the help of weak $P$-property and $P$-property, we proved existence and uniqueness of best proximity point. There is a simple example to show the validity of our results. Our results extended and unify many existing results in the literature. Moreover, an application to fractional order functional differential equation is discussed.<br /><br />

scholarly journals Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1594
Author(s):  
Antonio Francisco Roldán López de Hierro ◽  
Andreea Fulga ◽  
Erdal Karapınar ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Complete Metric Spaces ◽  
Auxiliary Functions ◽  
Fuzzy Metric ◽  
New Class

Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces.

Sign in / Sign up

Export Citation Format

Share Document