Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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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)
  • Received : 2010.08.19
  • Accepted : 2010.09.12
  • Published : 2010.09.30
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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

References

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