scholarly journals J-nonexpansive mappings in uniform spaces and applications

1991 ◽  
Vol 43 (2) ◽  
pp. 331-339 ◽  
Author(s):  
Vasil G. Angelov
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Functional Differential Equations ◽  
Uniform Convexity ◽  
Existence Theory ◽  
Uniform Spaces ◽  
Geometric Properties ◽  
Functional Differential

The purpose of the paper is to introduce a class of “j-nonexpansive” mappings and to prove fixed point theorems for such mappings. They naturally arise in the existence theory of functional differential equations. These mappings act in spaces without specific geometric properties as, for instance, uniform convexity. Critical examples are given.

scholarly journals Existence Results for Semilinear Functional Differential System with Nonlocal Conditions

2018 ◽  
Vol 8 (10S) ◽  
pp. 237-241
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Abstract Space ◽  
Functional Differential ◽  
Functional Differential System

In this paper, sufficient conditions are given for the existence of partial functional differential equations with nonlocal conditions in an abstract space with the help of the fixed point theorems.

scholarly journals Smooth Solutions of a Class of Iterative Functional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Houyu Zhao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Smooth Solutions ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

By Faà di Bruno’s formula, using the fixed-point theorems of Schauder and Banach, we study the existence and uniqueness of smooth solutions of an iterative functional differential equationx′(t)=1/(c0x[0](t)+c1x[1](t)+⋯+cmx[m](t)).

The Existence of Solutions for Fractional Functional Differential Equations With Boundary Value Conditions

2011 ◽  
Author(s):  
Chunhai Kou ◽  
Huacheng Zhou ◽  
Sijia Wu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

In this paper, we are concerned with the existence of solutions for a class of nonlinear fractional functional differential equations with boundary value conditions. Some existence results of solutions are obtained. Our analysis relies on some fixed point theorems. Finally, some examples are presented to illustrate the main results.

scholarly journals Existence of Positive Periodic Solutions for a Class of Higher-Dimension Functional Differential Equations with Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhang Suping ◽  
Jiang Wei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Higher Dimension ◽  
Positive Periodic Solutions ◽  
Krasnoselskii Fixed Point Theorem ◽  
Functional Differential

By employing the Krasnoselskii fixed point theorem, we establish some criteria for the existence of positive periodic solutions of a class ofn-dimension periodic functional differential equations with impulses, which improve the results of the literature.

Three Positive Periodic Solutions of Nonlinear Functional Differential Equations with Impulse Effects

2011 ◽  
Vol 403-408 ◽  
pp. 1319-1321
Author(s):  
Lei Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Nonlinear Functional ◽  
Functional Differential

In this paper, a type of nonlinear functional differential equations with impulse effects are studied by using the Leggett-Williams fixed point theorem.

scholarly journals Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”

2022 ◽  
Vol 27 (1) ◽  
pp. 163-178
Author(s):  
Mudasir Younis ◽  
Aleksandra Stretenović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Order ◽  
Metric Spaces ◽  
Functional Differential Equations ◽  
Contractive Condition ◽  
Nonlinear Anal ◽  
Model Control ◽  
Functional Differential ◽  
Picard Sequence

In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-ofart. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.

scholarly journals Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Lokesh Budhia ◽  
Hassen Aydi ◽  
Arslan Hojat Ansari ◽  
Dhananjay Gopal
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Existence Of A Solution ◽  
Rectangular Metric Space ◽  
Functional Differential

In this paper, we establish some new fixed point theorems for generalized ϕ–ψ-contractive mappings satisfying an admissibility-type condition in a Hausdorff rectangular metric space with the help of C-functions. In this process, we rectify the proof of Theorem 3.2 due to Budhia et al. [New fixed point results in rectangular metric space and application to fractional calculus, Tbil. Math. J., 10(1):91–104, 2017]. Some examples are given to illustrate the theorems. Finally, we apply our result (Corollary 3.6) to establish the existence of a solution for an initial value problem of a fractional-order functional differential equation with infinite delay. 

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