A certain ( p , q ) $(p,q)$ -derivative operator and associated divided differences

Abstract

Abstract Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator D q $D_{q}$ and divided difference. As applications of the post-quantum calculus known as the ( p , q ) $(p,q)$ -calculus, we derive several relations involving the ( p , q ) $(p,q)$ -derivative operator and divided differences.

Keywords

• q-calculus
• ( p , q ) $(p,q)$ -calculus
• divided differences
• ( p , q ) $(p,q)$ -derivative operator
• ( p , q ) $(p,q)$ -Leibniz rule
• principle of mathematical induction