2015 | OriginalPaper | Chapter
Theorem of Existence and Uniqueness of Fixed Points of Monotone Operators
Authors : Hui Luan, Zhihong Xia
Published in: Genetic and Evolutionary Computing
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Operator equation and the fixed point problem are an important component of nonlinear functional analysis theory. They are playing important role in solving nature and uniqueness problems about all kinds of differential equations and integral equations. Generally, the monotone operator has been defined with compactness, continuity and concavity and convexity in partially ordered Banach space. In this paper, without compactness and continuity, concavity and convexity of functions, a new fixed point theorem of increasing and decreasing operator and mixed monotone operator has obtained through introducing order-difference in the cone.