On Second Order q-Difference Equations Satisfied by Al-Salam–Carlitz I-Sobolev Type Polynomials of Higher Order

q-Karamata functions and second order q-difference equations

In this paper we introduce and study q-rapidly varying functions on the lattice q0 := {qk : k ∈ N0}, q > 1, which naturally extend the recently established concept of q-regularly varying functions. These types of functions together form the class of the so-called q-Karamata functions. The theory of q-Karamata functions is then applied to half-linear q-difference equations to get information abo...

Variational Iteration Method for q-Difference Equations of Second Order

Orthogonal matrix polynomials satisfying second order difference equations

We develop a method that allows us to construct families of orthogonal matrix polynomials of size N ×N satisfying second order difference equations with polynomial coefficients. The existence (and properties) of these orthogonal families strongly depends on the non commutativity of the matrix product, the existence of singular matrices and the matrix size N .

POSITIVE PERIODIC SOLUTIONS FOR HIGHER-ORDER FUNCTIONAL q-DIFFERENCE EQUATIONS

In this paper, using the recently introduced concept of periodic functions in quantum calculus, we study the existence of positive periodic solutions of a certain higher-order functional q-difference equation. Just as for the well-known continuous and discrete versions, we use a fixed point theorem in a cone in order to establish the existence of a positive periodic solution. This paper is dedi...

On Factorization and Solutions of q-difference Equations Satisfied by some Classes of Orthogonal Polynomials

Equations Satisfied by some Classes of Orthogonal Polynomials M. FOUPOUAGNIGNI*, W. KOEPF and A. RONVEAUX University of Yaounde I, Advanced School of Education, Department of Mathematics. P.O. Box 47 Yaounde, Cameroon; University of Kassel, Department of Mathematics and Computer Science, Heinrich-Plett Str. 40, 34132 Kassel, Germany; Facultés Universitaires Notre Dame de la Paix, B-5000 Namur, ...