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 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 Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Chatthai Thaiprayoon ◽  
Decha Samana ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Jump Conditions ◽  
Comparison Result ◽  
First Order ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Minimal And Maximal Solutions

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results.

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