scholarly journals Fixed Points for Multivalued Suzuki Type (θ,R)-Contraction Mapping with Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Mujahid Abbas ◽  
Hira Iqbal ◽  
Adrian Petrusel
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Contraction Mapping ◽  
Order Differential Equation ◽  
Existence Of A Solution ◽  
First Order ◽  
Fractional Differential ◽  
Homotopy Result

In this paper, we will introduce the concept of Suzuki type multivalued (θ,R)-contraction and we will prove some fixed point results in the setting of a metric space equipped with a binary relation. Our results generalize and extend various comparable results in the existing literature. Examples are provided to support the results proved here. As an application of our results, we obtain a homotopy result, proving the existence of a solution for a second-order differential equation and for a first-order fractional differential equation.

scholarly journals Solution of Fractional Differential Equations Utilizing Symmetric Contraction

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Aftab Hussain
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Differential Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Continuous Mappings ◽  
Fractional Differential ◽  
Fixed Point Technique

The aim of this paper is to present another family of fractional symmetric α - η -contractions and build up some new results for such contraction in the context of ℱ -metric space. The author derives some results for Suzuki-type contractions and orbitally T -complete and orbitally continuous mappings in ℱ -metric spaces. The inspiration of this paper is to observe the solution of fractional-order differential equation with one of the boundary conditions using fixed-point technique in ℱ -metric space.

scholarly journals Existence and uniqueness of solutions to a first-order differential equation via fixed point theorem in orthogonal metric space

2019 ◽  
pp. 123
Author(s):  
Madjid Eshaghi Gordji ◽  
Hasti Habibi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
The Other ◽  
Uniqueness Theorems ◽  
Uniqueness Of Solutions ◽  
First Order

In this paper, among the other things, we show that the solution of the first-orderdifferential equation is a fixed point of an integral operator from an orthogonal metric space into itself. This approach provides a new proof of the classical existence and uniqueness theorems of solutions to a first-order differential equation.

scholarly journals On Unique and Nonunique Fixed Points and Fixed Circles in M v b -Metric Space and Application to Cantilever Beam Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Meena Joshi ◽  
Anita Tomar ◽  
Hossam A. Nabwey ◽  
Reny George
Keyword(s):  
Differential Equation ◽  
Fixed Points ◽  
Metric Space ◽  
Order Differential Equation ◽  
Unique Fixed Point ◽  
Elastic Beam ◽  
Closed Ball ◽  
Open Ball ◽  
Ball Convergence ◽  
Fourth Order Differential Equation

We introduce M v b -metric to generalize and improve M v -metric and unify numerous existing distance notions. Further, we define topological notions like open ball, closed ball, convergence of a sequence, Cauchy sequence, and completeness of the space to discuss topology on M v b -metric space and to create an environment for the survival of a unique fixed point. Also, we introduce a notion of a fixed circle and a fixed disc to study the geometry of the set of nonunique fixed points of a discontinuous self-map and establish fixed circle and fixed disc theorems. Further, we verify all these results by illustrative examples to demonstrate the authenticity of the postulates. Towards the end, we solve a fourth order differential equation arising in the bending of an elastic beam.

scholarly journals Fixed point for F⊥-weak contraction

2021 ◽  
Vol 25 (1) ◽  
pp. 113-122
Author(s):  
Neeraj Garakoti ◽  
Joshi Chandra ◽  
Rohit Kumar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Order Differential Equation ◽  
Second Order ◽  
Weak Contraction ◽  
Second Order Differential Equation

In this paper, we establish some fixed point results for F⊥-weak contraction in orthogonal metric space and we give an application for the solution of second order differential equation.

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 New Existence of Fixed Point Results in Generalized Pseudodistance Functions with Its Application to Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 324 ◽  
Author(s):  
Sujitra Sanhan ◽  
Winate Sanhan ◽  
Chirasak Mongkolkeha
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Second Order ◽  
Second Order Differential Equation ◽  
Generalized Pseudodistance

The purpose of this article is to prove some existences of fixed point theorems for generalized F -contraction mapping in metric spaces by using the concept of generalized pseudodistance. In addition, we give some examples to illustrate our main results. As the application, the existence of the solution of the second order differential equation is given.

scholarly journals Fractional differential equation with uncertainty

2021 ◽  
Vol 23 (08) ◽  
pp. 181-185
Author(s):  
Karanveer Singh ◽  
◽  
R N Prajapati ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
First Order ◽  
Fractional Differential ◽  
First Order Differential Equations

We consider a fractional order differential equation with uncertainty and introduce the concept of solution. It goes beyond ordinary first-order differential equations and differential equations with uncertainty.

scholarly journals Fixed Points Results in G-Metric Spaces

2019 ◽  
Vol 32 (1) ◽  
pp. 142
Author(s):  
Salwa Salman Abed ◽  
Anaam Neamah Faraj ◽  
Anaam Neamah Faraj
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Closed Ball ◽  
Local Contraction

  In this paper, the concept of contraction mapping on a -metric space is extended with a consideration on local contraction.  As a result, two fixed point theorems were proved for contraction on a closed ball in a complete -metric space.

scholarly journals Fixed Point of Orthogonal F-Suzuki Contraction Mapping on O-Complete b-Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ismat Beg ◽  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fixed Point ◽  
Unique Solution ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Generalized Orthogonal

In this paper, we introduce the concept of generalized orthogonal F -Suzuki contraction mapping and prove some fixed point theorems on orthogonal b -metric spaces. Our results generalize and extend some of the well-known results in the existing literature. As an application of our results, we show the existence of a unique solution of the first-order ordinary differential equation.

scholarly journals Existence and Continuous Dependence on Initial Data of Solution for Initial Value Problem of Fuzzy Multiterm Fractional Differential Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Huichol Choi ◽  
Kinam Sin ◽  
Sunae Pak ◽  
Sungryol So
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Differential Equation ◽  
Continuous Dependence ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Existence Of Solution ◽  
Initial Value ◽  
Fractional Differential

In this paper, the fuzzy multiterm fractional differential equation involving Caputo-type fuzzy fractional derivative of order 0<α<1 is considered. The uniqueness of solution is established by using the contraction mapping principle and the existence of solution is obtained by Schauder fixed point theorem.

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