scholarly journals Controlled b-Branciari metric type spaces and related fixed point theorems with applications

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4253-4269
Author(s):  
Sumaiya Zubair ◽  
Kalpana Gopalan ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solution ◽  
Fixed Point Method ◽  
Fredholm Integral Equations ◽  
Effective Solution ◽  
Type Space ◽  
Type Spaces

In this manuscript, we present and develop different F-contraction methods using new kinds of contractions, namely F1-contraction and extended F1-contraction in the context of controlled b-Branciari metric type space. We then suggest an easy and effective solution for Fredholm integral equations using the fixed point method in the framework of controlled b-Branciari metric type space. We also provide an illustrative example for the existence of solution to second order boundary value problem to demonstrate the efficiency of the work that has been developed.

scholarly journals On a Fixed Point Theorem with Application to Integral Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Muhammad Nazam ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Existence Of Solution

We introduce the notion of dualistic Geraghty’s type contractions. We prove some fixed point theorems for ordered mappings satisfying the abovementioned contractions. We discuss an application of our fixed point results to show the existence of solution of integral equations.

scholarly journals On Quasi-Pseudometric Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Eniola Funmilayo Kazeem ◽  
Collins Amburo Agyingi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Cone Metric Space ◽  
Type Space ◽  
Type Spaces ◽  
Cone Metric

We introduce the concept of a quasi-pseudometric type space and prove some fixed point theorems. Moreover, we connect this concept to the existing notion of quasi-cone metric space.

scholarly journals On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 33
Author(s):  
Nizar Souayah ◽  
Mehdi Mrad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Partial Metric ◽  
Type Space ◽  
Type Spaces ◽  
Graphic Contraction ◽  
Kannan Contraction

Recently, Mlaiki et al. introduced the notion of a controlled metric type space which is a generalization of the b-metric space. In this work, we define the controlled partial metric type space and give some fixed-point theorems for extensions of Kannan contraction in this space with suitable conditions. Moreover, as an application, we derive a fixed-point theorem for graphic contraction on the considered metric space endowed with a graph.

On a class of nonlinear Volterra-Fredholm q-integral equations

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Zeinab Mansour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Fredholm Integral Equations ◽  
Banach Fixed Point Theorem ◽  
Continuous Solutions ◽  
Projective Metric ◽  
Uniqueness Criteria

AbstractIn this paper we investigate the existence and uniqueness of positive continuous solutions for a q-analogue of Volterra and Fredholm integral equations of first and second kinds. We derive the results by using three fixed point theorems introduced by Bushell in [7, 8]. Bushell derived his theorems by using the Cayley-Hilbert projective metric and Banach fixed point theorem. We also include some uniqueness criteria for the solutions of certain nonlinear q-integral equations provided that the solution exists in certain function spaces.

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 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 Fixed point method and its improvement for the system of Volterra-Fredholm integral equations of the second kind

MATEMATIKA ◽  
2017 ◽  
Vol 33 (2) ◽  
pp. 191
Author(s):  
Talaat Ismahel Hasan ◽  
Shaharuddin Salleh
Keyword(s):  
Fixed Point ◽  
Exact Solutions ◽  
Integral Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Fredholm Integral Equations ◽  
Numerical Examples ◽  
New Algorithms

In this paper, we consider the system of Volterra-Fredholm integral equations of the second kind (SVFI-2). We proposed fixed point method (FPM) to solve SVFI-2 and improved fixed point method (IFPM) for solving the problem. In addition, a few theorems and two new algorithms are introduced.  They are supported by numerical examples and simulations using Matlab. The results are reasonably good when compared with the exact solutions.

scholarly journals A Study on the Solutions of a Multiterm FBVP of Variable Order

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zoubida Bouazza ◽  
Sina Etemad ◽  
Mohammed Said Souid ◽  
Shahram Rezapour ◽  
Francisco Martínez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Research Study ◽  
Existence Of Solution ◽  
Variable Order ◽  
Order Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

In the present research study, for a given multiterm boundary value problem (BVP) involving the nonlinear fractional differential equation (NnLFDEq) of variable order, the uniqueness-existence properties are analyzed. To arrive at such an aim, we first investigate some specifications of this kind of variable order operator and then derive required criteria confirming the existence of solution. All results in this study are established with the help of two fixed-point theorems and examined by a practical example.

scholarly journals An Extended b -Metric-Type Space and Related Fixed Point Theorems with an Application to Nonlinear Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Nonlinear Integral Equations ◽  
Type Space ◽  
Contractive Mappings ◽  
Underlying Space

In this paper, the concept of sequential p -metric spaces has been introduced as a generalization of usual metric spaces, b -metric spaces and specially of p -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems.

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