Korean Journal of Mathematics

  • 제18권3호
  • /
  • Pages.299-309
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  • 2010
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  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

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)
  • 투고 : 2010.08.19
  • 심사 : 2010.09.12
  • 발행 : 2010.09.30
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초록

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.

키워드

참고문헌

  1. R. P. Agarwal, Difference Equations and Inequalities, Second Edition, Marcel Dekker, New York, 2000.
  2. M. P. Chen and B. G. Zhang, Oscillation and comparison theorems of difference equations with positive and negative coefficients, Bull. Inst. Math. Acad. Sin. (N.S.) 22 (1994), 295-306.
  3. B. S. Lalli and B. G. Zhang, On existence of positive solutions and bounded oscillations for neutral difference equations, J. Math. Anal. Appl. 166 (1992), 272-287. https://doi.org/10.1016/0022-247X(92)90342-B
  4. B. G. Zhang and H. Wang, The existence of oscillatory and nonoscillatory solution of neutral difference equation, Chinese J. Math. 24 (1996), 377-393.