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 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 Fixed Points forψ-Graphic Contractions with Application to Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. Hussain ◽  
S. Al-Mezel ◽  
P. Salimi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Partial Metric Spaces

The aim of this paper is to define modified weakα-ψ-contractive mappings and to establish fixed point results for such mappings defined on partial metric spaces using the notion of triangularα-admissibility. As an application, we prove new fixed point results for graphic weakψ-contractive mappings. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results.

scholarly journals Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Marin Borcut ◽  
Mădălina Păcurar ◽  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Nonlinear Mappings

We present new results on the existence and uniqueness of tripled fixed points for nonlinear mappings in partially ordered complete metric spaces that extend the results in the previous works: Berinde and Borcut, 2011, Borcut and Berinde, 2012, and Borcut, 2012. An example and an application to support our new results are also included in the paper.

scholarly journals Fixed Point Theorems for Geraghty Contraction Type Mappings in b-Metric Spaces and Applications

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 34 ◽  
Author(s):  
Hamid Faraji ◽  
Dragana Savić ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Nonlinear Integral Equations ◽  
Contractive Mappings ◽  
Contraction Type

In this paper, some new results are given on fixed and common fixed points of Geraghty type contractive mappings defined in b-complete b-metric spaces. Moreover, two examples are represented to show the compatibility of our results. Some applications for nonlinear integral equations are also given.

scholarly journals The Generalized Weaker(α-ϕ-φ)-Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Chi-Ming Chen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of generalized weaker(α-ϕ-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

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.

scholarly journals Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Santosh Kumar
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Integral Equations ◽  
Discontinuous Mappings ◽  
Contractive Maps ◽  
Uniqueness Of A Solution ◽  
Type Contraction

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra integral equations.

scholarly journals Solving a Class of Integral Equations via Contractive Mapping with Rational Type

2020 ◽  
Vol 13 (4) ◽  
pp. 995-1015
Author(s):  
Abdullah Abdullah ◽  
Muhammad Sarwar ◽  
Zead Mustafa ◽  
Mohammed M.M. Jaradat
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Mapping ◽  
Coupled Fixed Point Theorem ◽  
Set Up ◽  
Rational Type

In this paper, using rational type contractive conditions, the existence and uniqueness of common coupled fixed point theorem in the set up of Gb-metric spaces is studied. The derived result cover and generalize some well-known comparable results in the existing literature. Then we use the derived results to prove the existence and uniqueness solution for some classes of integral equations. Further more, an example of such type of integral equation is presented.

scholarly journals Common Fixed Points for Weakψ-Contractive Mappings in Ordered Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sumit Chandok ◽  
Simona Dinu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Contractive Mappings ◽  
Common Fixed Point Theorems

We obtain some new common fixed point theorems satisfying a weak contractive condition in the framework of partially ordered metric spaces. The main result generalizes and extends some known results given by some authors in the literature.

scholarly journals Periodic Points and Fixed Points for the Weaker(ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Chi-Ming Chen ◽  
W. Y. Sun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Periodic Points ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of weaker(ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

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