scholarly journals Solving singular coupled fractional differential equations with integral boundary constraints by coupled fixed point methodology

2021 ◽  
Vol 6 (12) ◽  
pp. 13370-13391
Author(s):  
Hasanen A. Hammad ◽  
◽  
Watcharaporn Chaolamjiak ◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Mapping ◽  
Integral Boundary ◽  
Boundary Constraints ◽  
Coupled Common Fixed Point ◽  
Fractional Differential ◽  
Fixed Point Techniques ◽  
Theoretical Results

<abstract><p>This manuscript was originally built to establish some coupled common fixed point results for rational contractive mapping in the framework of $ b $-metric spaces. Thereafter, the existence and uniqueness of the boundary value problem for a singular coupled fractional differential equation of order $ \nu $ via coupled fixed point techniques are discussed. At the last, some supportive examples to illustrate the theoretical results are presented.</p></abstract>

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 Coupled Coincidence Point Theorems for New Types of Mixed Monotone Multivalued Mappings in Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Chalongchai Klanarong ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Coupled Common Fixed Point ◽  
Recent Developments

We introduce and study new types of mixed monotone multivalued mappings in partially ordered complete metric spaces. We give relationships between those two types of mappings and prove their coupled fixed point and coupled common fixed point theorems in partially ordered complete metric spaces. Some examples of each type of mappings satisfying the conditions of the main theorems are also given. Our main result includes several recent developments in fixed point theory of mixed monotone multivalued mappings.

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 Related Results to Hybrid Pair of Mappings and Applications in Bipolar Metric Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
G. N. V. Kishore ◽  
K. P. R. Rao ◽  
A. Sombabu ◽  
R. V. N. S. Rao
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Mapping ◽  
Mixed Monotone Property ◽  
Contraction Mappings ◽  
Monotone Property ◽  
Partially Ordered ◽  
Multivalued Contraction ◽  
Hybrid Pair

In this paper, we introduce the concept of multivalued contraction mappings in partially ordered bipolar metric spaces and establish the existence of unique coupled fixed point results for multivalued contractive mapping by using mixed monotone property in partially ordered bipolar metric spaces. Some interesting consequences of our results are obtained.

scholarly journals A note on the paper "A fixed point theorems in Sb-metric spaces"

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3335-3346 ◽  
Author(s):  
Yumnam Rohen ◽  
Tatjana Dosenovic ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Common Fixed Point ◽  
Definition Of ◽  
Common Fixed Point Theorems ◽  
Theoretical Results

Very recently, N. Souayan and N. Mlaiki [Nazir Souayan and Nabil Mlaiki, A fixed point theorem in Sb-metric spaces, J. Math. Comput. Sci. 16 (2016), 131-139] and S. Sedghi et al. [S. Sedghi, A. Gholidahneb, T. Dosenovic, J. Esfahani, S. Radenovic, Common fixed point of four maps in Sb-metric spaces, to appear in J. Linear Topol. Algebra], introduced the concept of Sb-metric space as a generalization of S-metric space. In this paper, we modified the definition of Sb-metric introduced by Souayan and Mlaiki and prove some coupled common fixed point theorems in Sb-metric space. We also present an example to confirm our theoretical results.

scholarly journals A Unique Coupled Common Fixed Point Theorem for Symmetric(φ,ψ)-Contractive Mappings in OrderedG-Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Manish Jain ◽  
Kenan Taş
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Common Fixed Point ◽  
Contractive Mappings ◽  
Theoretical Results ◽  
Common Fixed Point Theorem

We establish the existence and uniqueness of coupled common fixed point for symmetric(φ,ψ)-contractive mappings in the framework of orderedG-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011), Nashine (2012), and Mohiuddine and Alotaibi (2012), thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.

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.

scholarly journals Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1168
Author(s):  
Hanadi Zahed ◽  
Hoda A. Fouad ◽  
Snezhana Hristova ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Integral Boundary ◽  
Complete Metric Spaces ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

The main objective of this paper is to introduce the ( α , β )-type ϑ -contraction, ( α , β )-type rational ϑ -contraction, and cyclic ( α - ϑ ) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2).

scholarly journals Some New Results on F-Contractions in 0-Complete Partial Metric Spaces and 0-Complete Metric-Like Spaces

2021 ◽  
Vol 5 (2) ◽  
pp. 34
Author(s):  
Stojan Radenović ◽  
Nikola Mirkov ◽  
Ljiljana R. Paunović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Partial Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Fractional Differential ◽  
Theoretical Results

Within this manuscript we generalize the two recently obtained results of O. Popescu and G. Stan, regarding the F-contractions in complete, ordinary metric space to 0-complete partial metric space and 0-complete metric-like space. As Popescu and Stan we use less conditions than D. Wardovski did in his paper from 2012, and we introduce, with the help of one of our lemmas, a new method of proving the results in fixed point theory. Requiring that the function F only be strictly increasing, we obtain for consequence new families of contractive conditions that cannot be found in the existing literature. Note that our results generalize and complement many well-known results in the fixed point theory. Also, at the end of the paper, we have stated an application of our theoretical results for solving fractional differential equations.

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