scholarly journals Ordered $S_{p}$-metric spaces and some fixed point theorems for contractive mappings with application to periodic boundary value problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Z. Mustafa ◽  
R. J. Shahkoohi ◽  
V. Parvaneh ◽  
Z. Kadelburg ◽  
M. M. M. Jaradat
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Contractive Mappings ◽  
Periodic Boundary Value Problems

Abstract In this paper, we introduce the structure of $S_{p}$ S p -metric spaces as a generalization of both S-metric and $S_{b}$ S b -metric spaces. Also, we present the notions of S̃-contractive mappings in the setup of ordered $S_{p}$ S p -metric spaces and investigate the existence of a fixed point for such mappings under various contractive conditions. We provide examples to illustrate the results presented herein. An application to periodic boundary value problems is presented.

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.

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.

scholarly journals Fixed Point Results forG-α-Contractive Maps with Application to Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Nawab Hussain ◽  
Vahid Parvaneh ◽  
Jamal Rezaei Roshan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
First Order ◽  
Contractive Mappings ◽  
Ordered Space ◽  
Contractive Maps

We unify the concepts ofG-metric, metric-like, andb-metric to define new notion of generalizedb-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes ofG-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results.

scholarly journals Positive Solutions to Periodic Boundary Value Problems for Four-Order Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Huantao Zhu ◽  
Zhiguo Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Periodic Boundary Value Problems

We apply fixed point theorem in a cone to obtain sufficient conditions for the existence of single and multiple positive solutions of periodic boundary value problems for a class of four-order differential equations.

scholarly journals Fixed point theorems via w-distance in relational metric spaces with an application

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1889-1898
Author(s):  
Gopi Prasad
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Binary Relation ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
First Order ◽  
Contractive Mappings

In this paper, we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance on metric spaces endowed with an arbitrary binary relation. Our fixed point theorems generalize recent results of Senapati and Dey [ J. Fixed Point Theory Appl., 19, 2945-2961, (2017)] and many other important results of the existing literature. Moreover, in order to revel the usability of our findings an example and an application to first order periodic boundary value problem are given.

scholarly journals Existence of Solutions for a Periodic Boundary Value Problem via Generalized Weakly Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sirous Moradi ◽  
Erdal Karapınar ◽  
Hassen Aydi
Keyword(s):  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Weakly Contractive

We discuss the existence of solutions for a periodic boundary value problem and for some polynomials. For this purpose, we present some fixed point theorems for weakly and generalized weakly contractive mappings in the setting of partially ordered complete metric spaces.

scholarly journals MULTIPLE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST-ORDER DIFFERENCE EQUATIONS

2008 ◽  
Vol 78 (1) ◽  
pp. 1-11
Author(s):  
DA-BIN WANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Multiple Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Order Difference ◽  
First Order ◽  
Periodic Boundary Value Problems

AbstractIn this paper, existence criteria for multiple solutions of periodic boundary value problems for the first-order difference equation are established by using the Leggett–Williams multiple fixed point theorem and fixed point theorem of cone expansion and compression. Two examples are also given to illustrate the main results.

Hyers–Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems

2019 ◽  
Vol 27 (3) ◽  
pp. 143-152
Author(s):  
A. Boudaoui ◽  
T. Caraballo ◽  
T. Blouhi
Keyword(s):  
Fixed Point ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Ulam Stability ◽  
Random Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Type ◽  
Stability Results

Abstract In this paper, we prove some existence, uniqueness and Hyers–Ulam stability results for the coupled random fixed point of a pair of contractive type random operators on separable complete metric spaces. The approach is based on a new version of the Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given.

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