CONVEX SOLUTIONS OF THE POLYNOMIAL-LIKE ITERATIVE EQUATION ON OPEN SET

Title & Authors
CONVEX SOLUTIONS OF THE POLYNOMIAL-LIKE ITERATIVE EQUATION ON OPEN SET
Gong, Xiaobing;

Abstract
Because of difficulty of using Schauder`s fixed point theorem to the polynomial-like iterative equation, a lots of work are contributed to the existence of solutions for the polynomial-like iterative equation on compact set. In this paper, by applying the Schauder-Tychonoff fixed point theorem we discuss monotone solutions and convex solutions of the polynomial-like iterative equation on an open set (possibly unbounded) in $\small{\mathbb{R}^N}$. More concretely, by considering a partial order in $\small{\mathbb{R}^N}$ defined by an order cone, we prove the existence of increasing and decreasing solutions of the polynomial-like iterative equation on an open set and further obtain the conditions under which the solutions are convex in the order.
Keywords
iterative equation;open set;order;increasing operator and decreasing operator;
Language
English
Cited by
1.
On a Zoltán Boros’ problem connected with polynomial-like iterative equations, Nonlinear Analysis: Real World Applications, 2015, 26, 56
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