The purpose of this paper is to provide a broad overview of the generalization of the various dualcomplex number sequences, especially in the disciplines of mathematics and physics. By the help of dual numbers and dualcomplex ...

In this study, we investigate the connection between second order recurrence matrix and several combinatorial matrices such as generalized r-eliminated Pascal matrix, Stirling matrix of the first and of the second kind ...

In this paper, we introduce the modified generalized Fibonacci and Lucas quaternions. We present the generating functions, the Binet formulas and some significant identities for these quaternions. ...

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 ...

Quantum calculus, which arises in the mathematical fields of combinatorics and special functions as well as in a number of areas, involving the study of fractals and multi-fractal measures, and expressions for the entropy ...