scholarly journals Fixed Point Theorems for Various Classes of Cyclic Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hassen Aydi ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems

We introduce new classes of cyclic mappings and we study the existence and uniqueness of fixed points for such mappings. The presented theorems generalize and improve several existing results in the literature.

scholarly journals Notes on multidimensional fixed-point theorems

2017 ◽  
Vol 50 (1) ◽  
pp. 360-374 ◽  
Author(s):  
Habibulla Akhadkulov ◽  
Salmi M. Noorani ◽  
Azizan B. Saaban ◽  
Fathilah M. Alipiah ◽  
Habes Alsamir
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Weak Contraction ◽  
Contraction Condition ◽  
Nonlinear Mappings

Abstract In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ, θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

scholarly journals Fixed point theorems in modular G-metric spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Daniel Francis ◽  
Manuel de la Sen ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Weakly Compatible ◽  
Special Cases

AbstractWe prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases.

Fixed point theorems for a pair of single-valued operators in a metric space endowed with a reflexive relation

2017 ◽  
Vol 33 (3) ◽  
pp. 301-310
Author(s):  
MELANIA-IULIA DOBRICAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Uniqueness Theorems ◽  
Mixed Monotone Property ◽  
First Order ◽  
System Equation ◽  
Coupled Fixed Points

In this paper we provide some existence and uniqueness theorems for coupled fixed points for a pair of contractive operators satisfying a mixed monotone property, in a metric space endowed with a reflexive relation. An application to a first-order differential system equation with PBV conditions is also given to illustrate the utility of our results.

scholarly journals Coupled Fixed Point Theorems with New Implicit Relations and an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Implicit Relation ◽  
Coupled Fixed Points

We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

scholarly journals Cyclic generalized φ-contractions in b-metric spaces and an application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2047-2057 ◽  
Author(s):  
Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Problem ◽  
Contractive Mappings

We introduce the notion of cyclic generalized ?-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.

scholarly journals New Fixed Point Results for Modified Contractions and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 660
Author(s):  
Hüseyİn Işık ◽  
Hassen Aydi ◽  
Mohd Salmi Md Noorani ◽  
Haitham Qawaqneh
Keyword(s):  
Functional Equation ◽  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Contractive Mapping ◽  
Graph Type ◽  
New Type

In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming.

Fixed point theorems of (α,ψ) G-contractive mappings in quasi-partial b-metric-like spaces endowed with a graph

2019 ◽  
pp. 2150014
Author(s):  
Anuradha Gupta ◽  
Manu Rohilla
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contractive Mappings

The notion of [Formula: see text] G-contractive mappings is defined and the existence and uniqueness of fixed points of such mappings on quasi-partial b-metric-like spaces endowed with a graph are obtained. An application and examples are provided to illustrate the results.

scholarly journals Fixed Point Theorems of Quasicontractions on Cone Metric Spaces with Banach Algebras

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hao Liu ◽  
Shaoyuan Xu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
New Method ◽  
Cone Metric Spaces ◽  
Cone Metric

We introduce the concept of quasicontractions on cone metric spaces with Banach algebras, and by a new method of proof, we will prove the existence and uniqueness of fixed points of such mappings. The main result generalizes the well-known theorem of Ćirić (Ćirić 1974).

scholarly journals Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 605-615 ◽  
Author(s):  
Peyman Salimi ◽  
Calogero Vetro ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Contractive Type

The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.

scholarly journals Alpha- F -Convex Contraction Mappings in b -Metric Space and a Related Fixed Point Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Kitila Wirtu Geleta ◽  
Kidane Koyas Tola ◽  
Solomon Gebregiorgis Teweldemedhin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contraction Mappings

In this paper, we establish fixed point theorems for α - F -convex contraction mappings in b -metric space and prove the existence and uniqueness of fixed points for such mappings. Our result extends and generalizes comparable results in the existing literature. Finally, we provide an example in support of our main finding.

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