Abstract
In this paper, by introducing the concept of a generalized concave operator and the properties of cone and monotone iterative technique in ordered Banach spaces, some new existence and uniqueness theorems of fixed points for the operator under more extensive conditions are obtained. Finally, as applications, we apply the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.

Keywords
fixed point; generalized concave operator; normal cone; positive solution; fractional differential equation; boundary value problems

Cite this paper
Fengxia Zheng, Fixed point theorems for generalized concave operators and applications to fractional differential equation boundary value problems , SCIREA Journal of Mathematics. Volume 2, Issue 3, December 2017 | PP. 41-54.

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