scholarly journals Random Fixed Point Theorems and Applications to Random First-Order Vector-Valued Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Adil El-Ghabi ◽  
Abdelmjid Khchine ◽  
Mohamed Aziz Taoudi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Random Operators ◽  
Random Fixed Point ◽  
First Order ◽  
Random Fixed Point Theorem ◽  
Vector Valued ◽  
Ordered Banach Spaces

In this paper, we establish several random fixed point theorems for random operators satisfying some iterative condition w.r.t. a measure of noncompactness. We also discuss the case of monotone random operators in ordered Banach spaces. Our results extend several earlier works, including Itoh’s random fixed point theorem. As an application, we discuss the existence of random solutions to a class of random first-order vector-valued ordinary differential equations with lack of compactness.

scholarly journals Fractional Partial Random Differential Equations with State-Dependent Delay

2017 ◽  
Vol 55 (1) ◽  
pp. 21-35
Author(s):  
Mouffak Benchohra ◽  
Amel Heris
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Darboux Problem ◽  
Random Fixed Point ◽  
State Dependent ◽  
State Dependent Delay ◽  
Random Differential Equations ◽  
Random Fixed Point Theorem

AbstractIn the present paper we provide some existence results for the Darboux problem of partial fractional random differential equations with state-dependent delay by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.

scholarly journals Random fixed point theorems for Ciric quasi contraction in cone random metric spaces

2015 ◽  
Vol 53 (1) ◽  
pp. 163-175
Author(s):  
G. S. Saluja
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Recent Result ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Random Operators ◽  
Random Fixed Point ◽  
Random Fixed Point Theorem

Abstract The purpose of this paper is to establish a common random fixed point theorem by using Ciric quasi contraction for two random operators in the framework of cone random metric spaces and also to obtain some random fixed point results as corollaries. Our results extend and generalize the corresponding recent result from the current existing literature.

scholarly journals Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Erdal Karapınar ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

scholarly journals Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 143
Author(s):  
Chayut Kongban ◽  
Poom Kumam ◽  
Juan Martínez-Moreno ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Random Fixed Point ◽  
Contractive Mappings ◽  
Random Differential Equations ◽  
Contractive Maps

The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.

scholarly journals Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces

1994 ◽  
Vol 7 (4) ◽  
pp. 569-580 ◽  
Author(s):  
Ismat Beg ◽  
Naseer Shahzad
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Random Operators ◽  
Random Coincidence ◽  
Random Fixed Point ◽  
Random Fixed Points ◽  
Multivalued Operators ◽  
Contractive Type

The existence of random fixed points. for nonexpansive and pseudocontractive random multivalued operators defined on unbounded subsets of a Banach space is proved. A random coincidence point theorem for a pair of compatible random multivalued operators is established.

scholarly journals Random Fixed Point Theorems of Random Comparable Operators and an Application

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Jiandong Yin ◽  
Zhongdong Liu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Monotone Operators ◽  
Hammerstein Integral Equation ◽  
Random Fixed Point ◽  
Partially Ordered ◽  
Ordered Banach Spaces

We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation.

scholarly journals Some Random Fixed-Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Kenza Benkirane ◽  
Abderrahim EL Adraoui ◽  
El Miloudi Marhrani
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Fixed Point Theorems ◽  
Stochastic Integral ◽  
Equation System ◽  
Random Operators ◽  
Stochastic Integral Equation ◽  
Random Fixed Point ◽  
Weakly Contractive ◽  
Uniqueness Of A Solution

The aim of this paper is to prove a common random fixed-point and some random fixed-point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a solution of a nonlinear stochastic integral equation system.

scholarly journals On the existence and Ulam-Hyers stability of a new class of partial (Φ,χ)-fractional differential equations with impulses

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1977-1991
Author(s):  
Arjumand Seemab ◽  
ur Mujeeb Rehman ◽  
Michal Feckan ◽  
Jehad Alzabut ◽  
Syed Abbas
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Stability Of Solutions ◽  
New Class ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

In this paper, we consider the newly defined partial (?,?)-fractional integral and derivative to study a new class of partial fractional differential equations with impulses. The existence and Ulam-Hyers stability of solutions for the proposed equation are investigated via the means of measure of noncompactness and fixed point theorems. The presented results are quite general in their nature and further complement the existing ones.

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