[KSCI] Korea Science Citation Index Service

EXISTENCE AND MANN ITERATIVE METHODS OF POSITIVE SOLUTIONS OF FIRST ORDER NONLINEAR NEUTRAL DIFFERENCE EQUATIONS

Hao, Jinbiao (Department of Mathematics Liaoning Normal University)
Kang, Shin Min (Department of Mathematics and RINS Gyeongsang National University)

Publication Information

Korean Journal of Mathematics / v.18, no.3, 2010 , pp. 299-309 More about this Journal

Abstract

In this paper, we study the first order nonlinear neutral difference equation: ${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$ . Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.

Keywords

first order nonlinear neutral difference equation; bounded positive solution; Banach fixed point theorem; Mann iterative scheme;

Citations & Related Records

Reference

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