The purpose of this paper is to provide a broad overview of thegeneralization of the various dual-complex number sequences, especially inthe disciplines of mathematics and physics. By the help of dual numbers and dual-complex ...

In recent years, many researchers have studied hyperbolic Fibonacci functions and some special polynomials, which are important areas of mathematics. In this study, we give an extension of the Euler polynomials in order ...

In this paper, we show that the following three-dimensional system of difference equations xn = zn−2xn−3 axn−3 + byn−1 , yn = xn−2 yn−3 cyn−3 + dzn−1 , zn = yn−2zn−3 ezn−3 + f xn−1 , n ∈ N0, where the parameters ...

Consider the three-dimensional system of difference equations xn+1 = ∏k j=0 zn−3j ∏k j=1 xn−(3j−1) ( an + bn ∏k j=0 zn−3j ), yn+1 = ∏k j=0 xn−3j ∏k j=1 yn−(3j−1) ( cn + dn ∏k j=0 xn−3j ), zn+1 = ∏k j=0 ...

Let fp;m be a real valued function on R, p be nonnegative integer, k be a positive integer and m be a nonnegative real number. For all x 2 R, fp;m(x + (p + 1)k) = mfp;m(x + pk) + fp;m(x), we call this function m􀀀�����extension ...

In this paper we show that the system of difference equations xn = ayn−k + dyn−kxn−(k+l) bxn−(k+l) + cyn−l , yn = αxn−k + δxn−kyn−(k+l) βyn−(k+l) + γxn−l , where n ∈ N0, k and l are positive integers, the parameters ...