scholarly journals Applications to Boundary Value Problems and Homotopy Theory via Tripled Fixed Point Techniques in Partially Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2012
Author(s):  
Hasanen A. Hammad ◽  
Praveen Agarwal ◽  
Juan L. G. Guirao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Unique Solution ◽  
Homotopy Theory ◽  
Metric Spaces ◽  
Boundary Value ◽  
Tripled Fixed Point ◽  
Fixed Point Techniques ◽  
Theoretical Results

In this manuscript, some tripled fixed point results were derived under (φ,ρ,ℓ)-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, some results about a homotopy results are obtained. Finally, theoretical results are involved in some applications, such as finding the unique solution to the boundary value problems and homotopy theory.

A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

2021 ◽  
pp. 1-21
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
A. Nafea
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Mixed Monotone Property ◽  
Cone Metric Spaces ◽  
System Of Integral Equations ◽  
Tripled Fixed Point ◽  
Fixed Point Techniques ◽  
Theoretical Results ◽  
Cone Metric

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

scholarly journals Wardowski’s Contraction and Fixed Point Technique for Solving Systems of Functional and Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Hasanen A. Hammad ◽  
Monica-Felicia Bota ◽  
Liliana Guran
Keyword(s):  
Fixed Point ◽  
Unique Solution ◽  
Integral Equations ◽  
Directed Graph ◽  
Metric Spaces ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Fixed Point Technique ◽  
Theoretical Results

In this manuscript, some tripled fixed point results are presented in the framework of complete metric spaces. Furthermore, Wardowski’s contraction was mainly applied to discuss some theoretical results with and without a directed graph under suitable assertions. Moreover, some consequences and supportive examples are derived to strengthen the main results. In the last part of the paper, the obtained theoretical results are used to find a unique solution to a system of functional and integral equations.

scholarly journals Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2267
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la De la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Control Function ◽  
Cone Metric Spaces ◽  
Tripled Fixed Point ◽  
Contractive Type ◽  
Theoretical Results ◽  
Cone Metric

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

scholarly journals New Contractive Mappings and Their Fixed Points in Branciari Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hayel N. Saleh ◽  
Mohammad Imdad ◽  
Thabet Abdeljawad ◽  
Mohammad Arif
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Contractive Mappings

In this paper, we introduce the notion of generalized L-contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of L∗-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.

scholarly journals Positive Solutions for Discrete Boundary Value Problems to One-Dimensionalp-Laplacian with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Linjun Wang ◽  
Xumei Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Numerical Examples ◽  
One Dimensional ◽  
Existence Of Positive Solutions ◽  
Krasnoselskii Fixed Point Theorem ◽  
Theoretical Results

We study the existence of positive solutions for discrete boundary value problems to one-dimensionalp-Laplacian with delay. The proof is based on the Guo-Krasnoselskii fixed-point theorem in cones. Two numerical examples are also provided to illustrate the theoretical results.

scholarly journals Existence of an approximate solution for a class of fractional multi-point boundary value problems with the derivative term

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yanbin Sang ◽  
Luxuan He
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Boundary Value Problems ◽  
Unique Solution ◽  
Fixed Point Theorems ◽  
Nonlinear Operator ◽  
Boundary Value ◽  
Point Boundary ◽  
Derivative Term ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution.

scholarly journals Some fixed point results for $ \alpha $-admissible extended $ \mathcal{Z} $-contraction mappings in extended rectangular $ b $-metric spaces

2021 ◽  
Vol 7 (3) ◽  
pp. 3701-3718
Author(s):  
Yan Sun ◽  
◽  
Xiao-lan Liu ◽  
Jia Deng ◽  
Mi Zhou ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Contraction Mappings

<abstract><p>In this paper, we introduce $ \alpha $-admissible extended $ \mathcal{Z} $-contraction in the extended rectangular $ b $-metric spaces, then we provide some other conditions in Theorem 3.1, which are different from that in Chifu et al. <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, and obtain the existence and uniqueness of fixed point in such spaces. Moreover, some examples are given to show the validity of our main theorems, and we give some corollaries related to our main results. As an application, we apply our main results to solve the existence of solutions for a class of boundary value problems of second order ordinary differential equations.</p></abstract>

Fixed point theorems in complete modular metric spaces and an application to anti-periodic boundary value problems

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5475-5488 ◽  
Author(s):  
Ümit Aksoy ◽  
Erdal Karapınar ◽  
İnci Erhan
Keyword(s):  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
Modular Metric Spaces ◽  
Periodic Boundary Value Problems ◽  
Theoretical Results

In this paper existence and uniqueness of fixed points for a general class of contractive and nonexpansive mappings on modular metric spaces is discussed. As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Carath?odory?s type is considered in the framework of modular metric spaces.

Solving a system of integral equations by using some tripled fixed point theorems

2020 ◽  
Vol 29 (1) ◽  
pp. 51-56
Author(s):  
MONICA LAURAN ◽  
ADINA POP
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
System Of Integral Equations ◽  
Tripled Fixed Point ◽  
Uniqueness Of A Solution ◽  
Theoretical Results

A tripled fixed point theorems in ordered metric spaces is used in order to prove the existence and uniqueness of a solution for a class of integral equations. The conditions of the theorem are much weaker than those existing in literature and the theorem is useful for solving some general problems. An example to illustrate our theoretical results is also given.

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