Abstract
By using the properties of cone and the fixed point theorem for mixed monotone operators in ordered Banach spaces, we investigate the mixed monotone operators of a new type with perturbation. We establish some sufficient conditions for such operators to have a new existence and uniqueness fixed point and provide monotone iterative techniques which give sequences convergent to the fixed point. Finally, as applications, we apple the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.
Highlights
Introduction and PreliminariesThe study of mixed monotone operators has been a lot of discussion since they were introduced by Guo and Lakshmikantham in 1987, because they have important theoretical meaning and wide applications in microeconomics, the nuclear industry, and so on
In the past several decades, many authors investigated these kinds of operators in ordered Banach spaces and obtained a lot of interesting and important fixed point theorems for mixed monotone operators, see [3,4,5] and the references therein
Without demanding the assumptions of the existence of coupled upper-lower solutions or compactness or continuity, we study mixed monotone operators with perturbation and give several of new fixed point theorems
Summary
Introduction and PreliminariesThe study of mixed monotone operators has been a lot of discussion since they were introduced by Guo and Lakshmikantham (see [1]) in 1987, because they have important theoretical meaning and wide applications in microeconomics, the nuclear industry, and so on (see [1, 2]).
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