on families of bounded continuous solutions of some systems of functional difference equations on half intervals some sufficient conditions for the existence of families of bounded continuous solutions of some classes of systems of functional difference equations on the intervals 0 and 0 are given

on continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument abstract bounded continuous solutions on r of a class of systems of nonlinear functional difference equations with a complicated nonlinear deviation of the argument that depends on unknown functions are studied here

a note on some higher order modifications of newton s method for solving nonlinear equations abstract in yoonmee ham changbum chun sang gu lee some higher order modifications of newtons method for solving nonlinear equations j comput appl math in press doi 10 1016 j cam 2007 11 018 a method to construct some higher order modifications of newton s method has been presented in this paper we show that the main result given by the authors is not accurate for p 1 and p 2 some counterexamples are given to verify our analysis

on some solvable systems of difference equations abstract we show that the following systems of difference equations x n 1 u n 1 v n y n 1 w n 1 s n n n 0 where u n v n w n s n are some of the sequences x n or y n with real initial values x 0 and y 0 are solvable in fourteen out of sixteen possible cases two cases are left unsolved probably the most interesting is the result in the case u n x n v n x n w n x n s n y n where a fascinating formula is obtained in an elegant way by using some ad hoc ideas

explicit nordsieck methods with extended stability regions abstract we describe the construction of explicit nordsieck methods of order p and stage order q p with large regions of absolute stability we also discuss error propagation and estimation of local discretization errors the error estimators are derived for examples of general linear methods constructed in this paper some numerical experiments are presented which illustrate the effectiveness of proposed methods

existence of monotone solutions of some difference equations with unstable equilibrium abstract we consider the difference equation x n 1 f x n x n 1 n 0 1 where the function f u v is continuous on i2 for some interval i 0 f 0 0 0 and f x x x for x i 0 assuming that f u c is decreasing in u on i and that f c v is increasing in v on i for any c i we establish a necessary and sufficient condition for existence of monotone solutions converging to the equilibrium x 0

unique existence of bounded continuous solutions on the real line of a class of nonlinear functional equations with complicated deviations abstract the existence and uniqueness of bounded continuous solutions on the real line of a general class of nonlinear functional equations with quite complicated deviations dependent of unknown functions are established in this paper

a note on some new iterative methods with third order convergence abstract in j h chen some new iterative methods with three order convergence appl math comput 181 2006 1519 1522 some new iterative methods were proposed and proved to be third order convergence in this paper some mistakes are pointed out in the derivation of these new methods an analysis is given to show that these new iterative methods converge only linearly

ball convergence comparison between three iterative methods in banach space under hypothese only on the first derivative we present a convergence ball comparison between three iterative methods for approximating a locally unique solution of a nonlinear equation in a banach space setting the convergence ball and error estimates are given for these methods under hypotheses only on the first frechet derivative in contrast to earlier studies such as adomian 1994 1 babajee et al 2008 13 cordero and torregrosa 2007 17 cordero et al 18 darvishi and barati 2007 19 using hypotheses reaching up to the fourth frechet derivative although only the first derivative appears in these methods this way we expand the applicability of these methods numerical examples are also presented in this study

existence uniqueness and attractivity of prime period two solution for a difference equation of exponential form abstract in this paper we study the existence uniqueness and attractivity of prime period two solution of the difference equation x n 1 a bx n 1 e x n where a b are positive constants and the initial values x 1 x 0 are positive numbers

on the difference equation xn xn kb cxn 1 xn k abstract we describe the behavior of well defined solutions of the difference equation x n x n k b cx n 1 x n k n n 0 where k n parameters b c and the initial values x k x 1 are real numbers these results among others improve and extend our results in s stevic more on a rational recurrence relation appl math e notes 4 2004 80 85

some new iterative methods with three order convergence some new iterative formulae having three order convergence are discussed in this paper the theoretical analysis and numerical experiments show that new iterative formulae are effective and comparable to well known method of newton and stefensen method

eventually constant solutions of a rational difference equation we describe all the solutions of a rational difference equation from putnam s mathematical competition which are eventually equal to its positive equilibrium email protected 1 as a consequence we give a new elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one moreover we show that almost all solutions of the equation are not eventually equal to one

on a third order system of difference equations abstract we show that the system of difference equations x n 1 a 1 x n 2 b 1 y n z n 1 x n 2 c 1 y n 1 a 2 y n 2 b 2 z n x n 1 y n 2 c 2 z n 1 a 3 z n 2 b 3 x n y n 1 z n 2 c 3 n n 0 where the parameters a i b i c i i 1 2 3 and initial values x j y j z j j 0 1 2 are real numbers can be solved developing further the results in the literature

on the recursive sequencexn 1 α xn 1 xn abstract we study the global stability the boundedness character and the periodic nature of the positive solutions of the difference equationxn 1 xn 1 xn where 0 and where the initial conditionsx 1andx0are arbitrary positive real numbers

on a class of quadratically convergent iteration formulae in this paper a new class of iterative formulae having quadratic convergence is presented furthermore these algorithms are comparable to the well known method of newton and the computed results support this theory

on the nonautonomous difference equation xn 1 an xn 1pxnq abstract in this paper we study the asymptotic behavior and the periodicity of the positive solutions of the nonautonomous difference equation x n 1 a n x n 1 p x n q n 0 1 where an is a positive bounded sequence p q 0 and x 1 x0 are positive numbers

on some linear difference equations and inequalities with continuous argument abstract we study some properties of solutions of linear difference equations and inequalities with continuous argument in terms of the location of the zeroes of the characteristic polynomial of the associated homogeneous linear difference equation with constant coefficients

a sixth order method for nonlinear equations abstract in this paper a sixth order method is developed by extending a third order method of weerakoon and fernando s weerakoon t g i fernando a variant of newton s method with accelerated third order convergence appl math lett 13 2000 87 93 for finding the real roots of nonlinear equations in r starting with a suitably chosen x 0 the method generates a sequence of iterates converging to the root the convergence analysis is provided to establish its sixth order of convergence in terms of computational cost it requires evaluations of only two functions and two first derivatives per iteration this implies that efficiency index of our method is 1 565 our method is comparable with the methods of neta b neta a sixth order family of methods for nonlinear equations intern j computer math 7 1979 157 161 and that of kou and li jisheng kou yitian li an improvement of jarratt method appl math comput 189 2007 1816 1821 it does not require the evaluation of the second order derivative of the given function as required in the family of chebyshev halley type methods jisheng kou xiuhua wang sixth order variants of chebyshev halley methods for solving non linear equations appl math comput 190 2007 1839 1843 jisheng kou on chebyshev halley methods with sixth order convergence for solving non linear equations appl math comput 190 2007 126 131 the efficacy of the method is tested on a number of numerical examples it is observed that our method takes less number of iterations than newton s method and the method of weerakoon and fernando on comparison with the other sixth order methods it behaves either similarly or better for the examples considered