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

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 51, Issue 3, 2014, pp.641-651
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2014.51.3.641

Title & Authors

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

Gong, Xiaobing;

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 . More concretely, by considering a partial order in 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

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