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arXiv · 2605.18412

Hadamard product of convex functions and Jackson operator

K. Piejko·J. Sokół·K. Trcabka-Wiȩc\a{l}aw
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Abstract

In this paper we consider some properties of Jackson's difference operator for convex univalent functions in $|z|<1$ with complex parameter $q$ as a Hadamard product of two power series. Jackson in 1908 introduced for a real $q$, $q\in[0,1)$, the difference operator \mbox{${\rm d}_qf(z)$} for an analytic function $f$ in the unit disc $|z|<1$ in the complex plane. Thanks to this operator, many mathematicians have extended the theory of functions in $q$-theory. The $q$-theory has found many applications in theory of hypergeometric series, special functions, combinatorics, number theory, fluid mechanics, quantum mechanics and physics.

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K. Piejko, J. Sokół, K. Trcabka-Wiȩc\a{l}aw. 2026-05-18. Hadamard product of convex functions and Jackson operator. https://arxiv.org/abs/2605.18412

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