Abstract
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.
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