Tripled fixed point results via a measure of noncompactness with applications
01 Feb 2021-Asian-european Journal of Mathematics (World Scientific Publishing Company)-Vol. 14, Iss: 02, pp 2150008
TL;DR: In this paper, a subjective measure of noncompactness in the sense of Banas and Goebel is used to create triplet fixed point outcomes via a subjective metric.
Abstract: In this paper, we create tripled fixed point outcomes via a subjective measure of noncompactness in the sense of Banas and Goebel. Furthermore, we introduce some applications of the measure of nonc...
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30 Sep 1996
TL;DR: In this paper, the authors propose nonlinear Integral Equations in Banach Spaces (i.e., nonlinear integral-differential Equations) and nonlinear Impulsive Integral Eq.
Abstract: Preface. 1. Preliminaries. 2. Nonlinear Integral Equations in Banach Spaces. 3. Nonlinear Integro-Differential Equations in Banach Spaces. 4. Nonlinear Impulsive Integral Equations in Banach Spaces. References.
463 citations
TL;DR: In this paper, the concept of triple fixed point was introduced for nonlinear mappings in partially ordered complete metric spaces and obtained existence and uniqueness theorems for contractive type mappings.
Abstract: In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393]. Examples to support our new results are given.
325 citations
TL;DR: In this paper, the authors focus on three fixed point theorems and an integral equation and prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T-periodic solution of (0.2) when / defines a contraction mapping, while D and g satisfy certain sign conditions independent of their magnitude.
Abstract: In this paper we focus on three fixed point theorems and an integral equation. Schaefer's fixed point theorem will yield a T-periodic solution of
(0.1) x(t)= a(t) + tt-h D(t,s)g(s,x(s))ds
if D and g satisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping theorem and Schauder's theorem (known as Krasnoselskii's theorem) will yield a T-periodic solution of
(0.2) x(t) = f(t,x(t)) + tt-h D(t,s)g(s,x(s))ds
if f defines a contraction and if D and g are small enough.
We prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T-periodic solution of (0.2) when / defines a contraction mapping, while D and g satisfy the aforementioned sign conditions.
162 citations
TL;DR: In this paper, the authors apply the technique of measures of noncompactness to the theory of infinite system of differential equations in the Banach sequence spaces l p (1 ≤ p ∞ ).
Abstract: In this paper we apply the technique of measures of noncompactness to the theory of infinite system of differential equations in the Banach sequence spaces l p ( 1 ≤ p ∞ ) . Our aim is to present some existence results for infinite system of differential equations formulated with the help of measures of noncompactness.
137 citations