scholarly journals Some Results for the Family KKM(X,Y) and the Φ-Mapping in FC-Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Rong-Hua He
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Minimax Theorems ◽  
Contraction Map ◽  
Coincidence Theorems ◽  
The Family ◽  
Compact Map

We first establish a fixed point theorem for a k-set contraction map on the family KKM(X,X), which does not need to be a compact map. Next, we present the KKM type theorems, matching theorems, coincidence theorems, and minimax theorems on the family KKM(X,Y) and the Φ-mapping in FC-spaces. Our results improve and generalize some recent results.

On the Homotopy Property of Nussbaum's Fixed Point Index

1982 ◽  
Vol 34 (1) ◽  
pp. 44-62
Author(s):  
Gilles Fournier ◽  
Reine Fournier
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Index ◽  
Point Index ◽  
Homotopy Property ◽  
Lefschetz Fixed Point Theorem ◽  
The One ◽  
Compact Map ◽  
General Conditions

In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.

A generalization of Krasnosel’skii fixed point theorem for sums of compact and contractible maps with application

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Bogdan Przeradzki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Generalized Contraction ◽  
Nonlinear Integral Equations ◽  
Bounded Set ◽  
Compact Map

AbstractThe existence of a fixed point for the sum of a generalized contraction and a compact map on a closed convex bounded set is proved. The result is applied to a kind of nonlinear integral equations.

Ulam stability of some functional inclusions for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5489-5495 ◽  
Author(s):  
Janusz Brzdęk ◽  
Magdalena Piszczek
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Main Tool ◽  
Ulam Stability ◽  
Nonlinear Operators ◽  
The Family ◽  
Fixed Positive Integer

We show that some multifunctions F : K ? n(Y), satisfying functional inclusions of the form ? (x,F(?1(x)),..., F(?n(x)))? F(x)G(x), admit near-selections f : K ? Y, fulfilling the functional equation ? (x,f (?1(x)),..,, f(?n(x)))= f(x), where functions G : K ? n(Y), ?: K x Yn ? Y and ?1,..., ?n ? KK are given, n is a fixed positive integer, K is a nonempty set, (Y,?) is a group and n(Y) denotes the family of all nonempty subsets of Y. Our results have been motivated by the notion of Ulam stability and some earlier outcomes. The main tool in the proofs is a very recent fixed point theorem for nonlinear operators, acting on some spaces of multifunctions.

scholarly journals On the existence of mild solutions for nonlocal differential equations of the second order with conformable fractional derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mustapha Atraoui ◽  
Mohamed Bouaouid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Conformable Fractional Derivative ◽  
The Family ◽  
Krasnoselskii Fixed Point Theorem

AbstractIn the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019), the authors have used the Krasnoselskii fixed point theorem for showing the existence of mild solutions of an abstract class of conformable fractional differential equations of the form: $\frac{d^{\alpha }}{dt^{\alpha }}[\frac{d^{\alpha }x(t)}{dt^{\alpha }}]=Ax(t)+f(t,x(t))$ d α d t α [ d α x ( t ) d t α ] = A x ( t ) + f ( t , x ( t ) ) , $t\in [0,\tau ]$ t ∈ [ 0 , τ ] subject to the nonlocal conditions $x(0)=x_{0}+g(x)$ x ( 0 ) = x 0 + g ( x ) and $\frac{d^{\alpha }x(0)}{dt^{\alpha }}=x_{1}+h(x)$ d α x ( 0 ) d t α = x 1 + h ( x ) , where $\frac{d^{\alpha }(\cdot)}{dt^{\alpha }}$ d α ( ⋅ ) d t α is the conformable fractional derivative of order $\alpha \in\, ]0,1]$ α ∈ ] 0 , 1 ] and A is the infinitesimal generator of a cosine family $(\{C(t),S(t)\})_{t\in \mathbb{R}}$ ( { C ( t ) , S ( t ) } ) t ∈ R on a Banach space X. The elements $x_{0}$ x 0 and $x_{1}$ x 1 are two fixed vectors in X, and f, g, h are given functions. The present paper is a continuation of the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019) in order to use the Darbo–Sadovskii fixed point theorem for proving the same existence result given in (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019) [Theorem 3.1] without assuming the compactness of the family $(S(t))_{t>0}$ ( S ( t ) ) t > 0 and any Lipschitz conditions on the functions g and h.

scholarly journals Some Variants of Krasnoselskii-Type Fixed Point Results for Equiexpansive Mappings with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Niaz Ahmad ◽  
Nayyar Mehmood ◽  
Ahmed Al-Rawashdeh
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
General Setting ◽  
Controlled System ◽  
The Family ◽  
Krasnoselskii Fixed Point Theorem ◽  
Evolution Differential Equation

In this paper, we investigate the Krasnoselskii-type fixed point results for the operator F of two variables by assuming that the family F x , . : x is equiexpansive. The results may be considered as variants of the Krasnoselskii fixed point theorem in a general setting. We use our main results to obtain the existence of solutions of a fractional evolution differential equation. An example of a controlled system is given to illustrate the application.

scholarly journals A coupled common fixed point theorem for a family of mappings

2013 ◽  
Vol 18 (1) ◽  
pp. 14-26 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Pradyut Das
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Coupled Fixed Point ◽  
Fixed Point Problems ◽  
Coupled Common Fixed Point ◽  
The Family ◽  
Common Fixed Point Theorem

In this paper we introduce the concept of coincidentally commuting pair in the context of coupled fixed point problems. It is established that an arbitrary family of mappings has a coupled common fixed point with two other functions under certain contractive inequality condition where two specific members of the family are assumed to be coincidentally commuting with these two functions respectively. The main result has certain corollaries. An example shows that the main theorem properly contains one of its corollaries.

scholarly journals On coincidence theorems for a family of mappings in convex metric spaces

1987 ◽  
Vol 10 (3) ◽  
pp. 453-460
Author(s):  
Olga Hadzic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Spaces ◽  
Coincidence Theorems ◽  
Common Fixed Point Theorem

In this paper, a theorem on common fixed points for a family of mappings defined on convex metric spaces is presented. This theorem is a generalization of the well known fixed point theorem proved by Assad and Kirk. As an application a common fixed point theorem in metric spaces with a convex structure is obtained.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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