On the Existence and Uniqueness of Fixed Points for Holomorphic Maps in Complex Banach Spaces

1991 ◽  
Vol 112 (4) ◽  
pp. 983
Author(s):  
Kazimierz Wlodarczyk
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Holomorphic Maps

scholarly journals On the Extensions of Krasnoselskii-Type Theorems top-Cyclic Self-Mappings in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Ad Hoc ◽  
Best Proximity Points

A set ofnp(≥2)-cyclic and either continuous or contractive self-mappings, with at least one of them being contractive, which are defined on a set of subsets of a Banach space, are considered to build a composed self-mapping of interest. The existence and uniqueness of fixed points and the existence of best proximity points, in the case that the subsets do not intersect, of such composed mappings are investigated by stating and proving ad hoc extensions of several Krasnoselskii-type theorems.

scholarly journals Some fixed point theorems for multivalued maps in ordered Banach spaces and applications

2005 ◽  
Vol 2005 (20) ◽  
pp. 3247-3259
Author(s):  
Zhai Chengbo ◽  
Yang Chen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Necessary And Sufficient Condition ◽  
Multivalued Maps ◽  
Necessary And Sufficient ◽  
Convex Operators ◽  
Ordered Banach Spaces

The existence of maximal and minimal fixed points for various set-valued operators is discussed. This paper presents some new fixed point theorems in ordered Banach spaces. A necessary and sufficient condition for the existence of the fixed point to a class of multivalued maps has been obtained. The uniqueness of the positive fixed point has been discussed. The results extend and improve the corresponding results. As an application, we utilize the results to study the existence and uniqueness of positive fixed points for a class of convex operators. In the end, we give a simple application to certain integral equations.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

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