Results on the \(q\)-type \(k\)-Lidstone polynomials

Volume 37, Issue 1, pp 82--93 https://dx.doi.org/10.22436/jmcs.037.01.06

Publication Date: September 13, 2024 Submission Date: September 08, 2023 Revision Date: April 01, 2024 Accteptance Date: August 01, 2024

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Authors

M. Al-Towailb - Department of Computer Science and Engineering‎, ‎College of‎ ‎ Applied Studies and Community Service, ‎King Saud University, ‎Riyadh, KSA.

Abstract

‎In this paper‎, ‎we generalize the class of \(q\)-completely convex functions for Jackson \(q^{-1}\)-difference operator‎. ‎We study the relation of this class to the problem of representation of functions by a \(q\)-type \(k\)-Lidstone series‎. ‎Moreover‎, ‎we provide some results for the fundamental polynomials that appear in the \(q\)-type \(k\)-Lidstone series expansion‎. ‎In particular‎, ‎we present these polynomials based on Green’s function of a certain \(q\)-differential equation‎.

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Keywords

• \(q\)-Calculus
• \(q\)-differential operator
• Lidstone polynomials
• completely convex functions

MSC

•  05A30
•  41A58
•  39A70
•  40A05
•  11B83

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