Abstract
AbstractIn this paper, we firstly establish the existence and uniqueness of solutions of the operator equation $A(x,x)+ B(x,x)+C(x)+e = x$
A
(
x
,
x
)
+
B
(
x
,
x
)
+
C
(
x
)
+
e
=
x
, where A and B are two mixed monotone operators, C is a decreasing operator, and $e\in P$
e
∈
P
with $\theta \leq e \leq h$
θ
≤
e
≤
h
. Then, using our abstract theorem, we prove a class of fractional boundary value problems with the derivative term to have a unique solution and construct the corresponding iterative sequences to approximate the unique solution.
Funder
the Programs for the Cultivation of Young Scientific Research Personnel of Higher Education Institutions in Shanxi Province
the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi
the Innovative Research Team of North University of China
the Fund for Shanxi '1331KIRT'
Natural Science Foundation of Shanxi Province
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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