2–Cone Banach spaces and fixed point theorem

2012 ◽  
Author(s):  
Ahmet Sahiner ◽  
Tuba Yigit
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem

Simulation functions and Meir–Keeler condensing operators with application to integral equations

2021 ◽  
Author(s):  
Moosa Gabeleh ◽  
Mehdi Asadi ◽  
Pradip Ramesh Patle
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Darbo’S Fixed Point Theorem ◽  
Simulation Functions ◽  
Condensing Operators

We propose a new concept of condensing operators by using a notion of measure of non-compactness in the setting of Banach spaces and establish a new generalization of Darbo’s fixed point theorem. We also show the applicability of our results to integral equations. A concrete example will be presented to support the application part.

Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

2018 ◽  
Vol 27 (1) ◽  
pp. 37-48
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
LASZLO BALOG ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Condition

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

A FIXED POINT THEOREM IN BANACH SPACES OVER TOPOLOGICAL SEMIFIELDS AND AN APPLICATION

1999 ◽  
Vol 32 (1) ◽  
Author(s):  
H. K. Pathak ◽  
V. V. S. N. Lakshmi ◽  
Kenan Taş ◽  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem

ON APPROXIMATELY ADDITIVE MAPPINGS IN 2-BANACH SPACES

2019 ◽  
Vol 101 (2) ◽  
pp. 299-310 ◽  
Author(s):  
JANUSZ BRZDĘK ◽  
EL-SAYED EL-HADY
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Stability Result ◽  
Main Tool ◽  
Ulam Stability ◽  
Cauchy Equation ◽  
Stability Issues ◽  
Additive Mappings

We show how some Ulam stability issues can be approached for functions taking values in 2-Banach spaces. We use the example of the well-known Cauchy equation $f(x+y)=f(x)+f(y)$, but we believe that this method can be applied for many other equations. In particular we provide an extension of an earlier stability result that has been motivated by a problem of Th. M. Rassias. The main tool is a recent fixed point theorem in some spaces of functions with values in 2-Banach spaces.

Global solutions for Volterra ordinary and retarded integral equations

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Bianca Satco
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Global Solutions ◽  
Volterra Type ◽  
Darbo’S Fixed Point Theorem ◽  
Type Integral

AbstractUsing a generalization of Darbo’s fixed point theorem, we obtain the existence of global solutions for nonlinear Volterra-type integral equations in Banach spaces. The involved functions are supposed to be continuous only with respect to some variables, integrability or essential boundedness conditions being also imposed. Our result improves the similar result given in [

scholarly journals Null controllability of neutral evolution integrodifferential systems with infinite delay

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
K. Balachandran ◽  
A. Leelamani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Null Controllability ◽  
Neutral Evolution ◽  
Sadovskii Fixed Point Theorem

We establish a set of sufficient conditions for the controllability of nonlinear neutral evolution integrodifferential systems with infinite delay in Banach spaces. The results are established by using the Sadovskiĭ fixed point theorem and generalize the previous results.

Fixed point theorem for non-expansive mappings on banach spaces with uniformly normal structure

1979 ◽  
Vol 9 (2) ◽  
pp. 121-124 ◽  
Author(s):  
A. A. Gillespie ◽  
B. B. Williams ◽  
V. Lakshmikantham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Normal Structure
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