Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid Polynomials

Abstract

In this article, we construct a new type of degenerate q-sigmoid (DQS) polynomial for sigmoid functions containing quantum numbers and find several difference equations related to it. We check how each point moves by iteratively synthesizing a quartic degenerate q-sigmoid (DQS) polynomial that appears differently depending on q in the space of a complex structure. We also construct Julia sets associated with quartic DQS polynomials and find their features. Based on this, we make some conjectures.

Keywords

• (<i>q</i>,<i>h</i>)-derivative
• (<i>q</i>,<i>h</i>)-difference equations
• DQS polynomials
• Julia set