scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

scholarly journals Multivalued fixed point theorem in b-metric spaces and its application to differential inclusions

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2963-2976
Author(s):  
Maher Berzig ◽  
Imed Kédim ◽  
Aymen Mannai
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Multivalued Mappings ◽  
Point Problem ◽  
Contractive Condition ◽  
Well Posedness ◽  
Shadowing Property ◽  
Limit Shadowing

Our purpose in this paper is to present a fixed point result for multivalued mappings satisfying nonlinear quasi-contractive condition only on related points. Moreover, we provide a qualitative study of well-posedness, limit shadowing property and Ulam-Hyers stability of our fixed point problem. As application, we discuss the existence of a unique solution for a class of differential inclusions.

scholarly journals Generalized Ulam-Hyers Stability, Well-Posedness, and Limit Shadowing of Fixed Point Problems forα-β-Contraction Mapping in Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Well Posedness ◽  
Banach Contraction ◽  
Limit Shadowing ◽  
New Type ◽  
The Banach Contraction Principle

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-calledα-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

On the theory of fixed point theorems for convex contraction mappings

2015 ◽  
Vol 31 (3) ◽  
pp. 365-371
Author(s):  
VIORICA MURESAN ◽  
◽  
ANTON S. MURESAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Shadowing Property ◽  
Contraction Mappings ◽  
Limit Shadowing

Based on the concepts and problems introduced in [Rus, I. A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559], in the present paper we consider the theory of some fixed point theorems for convex contraction mappings. We give some results on the following aspects: data dependence of fixed points; sequences of operators and fixed points; well-posedness of a fixed point problem; limit shadowing property and Ulam-Hyers stability for fixed point equations.

scholarly journals Basic problems of the metric fixed point theory and the relevance of a metric fixed point theorem

2013 ◽  
Vol 29 (2) ◽  
pp. 239-258
Author(s):  
IOAN A. RUS ◽  
◽  
MARCEL-ADRIAN SERBAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
The Impact

In this paper we present some basic problems of the metric fixed point theory (existence, uniqueness, settheoretic aspects (Bessaga, Janos, Rus, ...), order-theoretic aspects (Ekeland, Bronsted, Caristi, Kirk, Jachymski, ...), convergence of the succesive approximations, data dependence (general estimation, Ulam problem, dependence on the parameters, ...), well-posedness of the fixed point problem, limit shadowing property, stability, Gronwall lemmas, comparison lemmas, retractibility, ...). Following [I. A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559] we define the relevance of a metrical fixed point theorem by the impact of the theorem on these basic problems. Some case studies are presented.

scholarly journals The theory of some asymptotic fixed point theorems

2014 ◽  
Vol 30 (3) ◽  
pp. 361-368
Author(s):  
ANTON S. MURESAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Point Problem ◽  
Shadowing Property ◽  
Contraction Mappings ◽  
Limit Shadowing ◽  
Asymptotic Fixed Point

In this paper we present the theory about some fixed point theorems for convex contraction mappings. We give some results on data dependence of fixed points, on sequences of operators and fixed points, on well-possedness of fixed point problem, on limit shadowing property and on Ulam-Hyers stability for equations of fixed points.

scholarly journals Multivalued Problems, Orthogonal Mappings, and Fractional Integro-Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
R. K. Sharma ◽  
Sumit Chandok
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Existence Of Solution ◽  
Point Problem ◽  
Contraction Mappings ◽  
Integro Differential Equation

In this manuscript, we propose some sufficient conditions for the existence of solution for the multivalued orthogonal ℱ -contraction mappings in the framework of orthogonal metric spaces. As a consequence of results, we obtain some interesting results. Also as application of the results obtained, we investigate Ulam’s stability of fixed point problem and present a solution for the Caputo-type nonlinear fractional integro-differential equation. An example is also provided to illustrate the usability of the obtained results.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

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