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In this paper we study fixed points of sums of α-concave and (−α)-convex operators in γ-complete partially ordered linear spaces. As an application we obtain existence and uniqueness theorems for solutions of a certain type of nonlinear integral equation.

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

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.3247 ◽

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.

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