In this paper, some new partially ordered Banach spaces are introduced.
Based on those new partially ordered Banach spaces and applying some fixed
point theorems, we present a new approach to the theory of nonlinear
sequential fractional differential equations. An example illustrating our
approach is also discussed.
We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation.
AbstractIn this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone $\mathbb{K}$
K
is normal, and then proceed to prove some coupled fixed point theorems in partially ordered Banach spaces. We relax the conditions of a proper domain of an underlying operator for partially ordered Banach spaces. Furthermore, we discuss an application to the existence of a local fractional integral equation.
Existence of periodic solutions for impulsive evolution equations in ordered Banach spaces
