Existence and uniqueness of fixed points for monotone operators in partially ordered Banach spaces and applications

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Mohamed Khazou ◽  
Mohamed Aziz Taoudi
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Monotone Operators ◽  
Partially Ordered ◽  
Ordered Banach Spaces

scholarly journals Random Fixed Point Theorems of Random Comparable Operators and an Application

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Jiandong Yin ◽  
Zhongdong Liu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Monotone Operators ◽  
Hammerstein Integral Equation ◽  
Random Fixed Point ◽  
Partially Ordered ◽  
Ordered Banach Spaces

We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation.

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.

A new criterion for the existence of multiple solutions in cones

2012 ◽  
Vol 142 (5) ◽  
pp. 1043-1050 ◽  
Author(s):  
Daniel Franco ◽  
Gennaro Infante ◽  
Juan Perán
Keyword(s):  
Boundary Value Problem ◽  
Fixed Points ◽  
Banach Spaces ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Sufficient Conditions ◽  
Extra Information ◽  
New Criterion ◽  
Multiple Fixed Points ◽  
Ordered Banach Spaces

We provide new sufficient conditions for the existence of multiple fixed points for a map between ordered Banach spaces. An interesting feature of this approach is that we require conditions not on two boundaries, but rather on one boundary and a point with some extra information on the monotonicity of the nonlinearity on a certain set. We apply our results to prove the existence of at least two positive solutions for a nonlinear boundary-value problem that models a thermostat.

Sign in / Sign up

Export Citation Format

Share Document