scholarly journals C*-Algebra Valued Partial b-Metric Spaces and Fixed Point Results with an Application

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1381
Author(s):  
Nabil Mlaiki ◽  
Mohammad Asim ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fredholm Integral Equations ◽  
Partial Metric ◽  
C Algebra ◽  
Partial Metric Spaces ◽  
Uniqueness Of A Solution

In this paper, we enlarge the class of C*-algebra valued partial metric spaces as well as the class of C*-algebra valued b-metric spaces by introducing the class of C*-algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm integral equations.

scholarly journals Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 49 ◽  
Author(s):  
Atiya Perveen ◽  
Idrees A. Khan ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Binary Relation ◽  
Metric Spaces ◽  
Partial Metric ◽  
System Of Integral Equations ◽  
Partial Metric Spaces ◽  
Nonlinear Contractions

In this paper, by introducing the concept of generalized Ćirić-type weak ( ϕ g , R ) -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.

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 Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Daniel Francis
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fredholm Integral Equations ◽  
Fredholm Type ◽  
Content Type ◽  
Special Cases ◽  
Type Integral ◽  
Social Applications

PurposeThe authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.Research limitations/implicationsThe results are theoretical and analytical.Practical implicationsThe results were applied to solving nonlinear integral equations.Social implicationsThe results has several social applications.Originality/valueThe results of this paper are new.

scholarly journals Fixed-Point Theorem for Nonlinear F -Contraction via w -Distance

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Fredholm Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Uniqueness Of A Solution

The aim of this paper is to introduce a notion of ϕ , F -contraction defined on a metric space with w -distance. Moreover, fixed-point theorems are given in this framework. As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations. Some illustrative examples are provided to advocate the usability of our results.

scholarly journals Coupled Fixed Point Theorems for Nonlinear Contractions in Partial Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Sharifa Al-Sharif ◽  
Mohammad Al-Khaleel ◽  
Mona Khandaqji
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Nonlinear Contractions

We establish some results on the existence and uniqueness of coupled fixed point involving nonlinear contractive conditions in complete-ordered partial metric spaces.

scholarly journals Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Hassen Aydi ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Coupled Fixed Point Theorem ◽  
Partial Metric Spaces ◽  
Ordered Partial Metric Space ◽  
Coupled Fixed Points

In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappingsF:X×X→Xandg:X→Xon a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012) have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012).

scholarly journals A study of common fixed points that belong to zeros of a certain given function with applications

2021 ◽  
Vol 26 (5) ◽  
pp. 781-800
Author(s):  
Hayel N. Saleh ◽  
Mohammad Imdad ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Uniqueness Result ◽  
Partial Metric ◽  
System Of Integral Equations ◽  
Partial Metric Spaces ◽  
Simulation Functions

In this paper, we establish some point of φ-coincidence and common φ-fixed point results for two self-mappings defined on a metric space via extended CG-simulation functions. By giving an example we show that the obtained results are a proper extension of several well-known results in the existing literature. As applications of our results, we deduce some results in partial metric spaces besides proving an existence and uniqueness result on the solution of system of integral equations.

scholarly journals Fixed Point Results in Partial Symmetric Spaces with an Application

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 13 ◽  
Author(s):  
Mohammad Asim ◽  
A. Khan ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Symmetric Spaces ◽  
Fixed Point Theorems ◽  
Hausdorff Metric ◽  
Contraction Principle ◽  
Fredholm Integral Equations ◽  
Uniqueness Of A Solution

In this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of Fredholm integral equations. Furthermore, we introduce an analogue of the Hausdorff metric in the context of partial symmetric spaces and utilize the same to prove an analogue of the Nadler contraction principle in such spaces. Our results extend and improve many results in the existing literature. We also give some examples exhibiting the utility of our newly established results.

scholarly journals On New χ -Fixed Point Results for λ − Υ , χ -Contractions in Complete Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Babak Mohammadi ◽  
Wutiphol Sintunavarat ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Partial Metric ◽  
Nonlinear Integral Equations ◽  
Complete Metric Spaces ◽  
Partial Metric Spaces ◽  
Theoretical Results

The main aim of this work is to introduce the new concept of λ − Υ , χ -contraction self-mappings and prove the existence of χ -fixed points for such mappings in metric spaces. Our results generalize and improve some results in existing literature. Moreover, some fixed point results in partial metric spaces can be derived from our χ -fixed points results. Finally, the existence of solutions of nonlinear integral equations is investigated via the theoretical results in this work.

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