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Certain Constraints for Functions Provided by Touchard Polynomials

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  • Tariq Al-Hawary
  • Mohamed Illafe
  • Feras Yousef

Abstract

Since finding solutions to integral equations is usually challenging analytically, approximate methods are often required, one of which is based on Touchard polynomials. This paper examines the necessary constraints for the functions Ϝετς,Πε,τ,ςℏ, and the integral operator Lετς, defined by Touchard polynomials, to be in the comprehensive subclass ∁η(q3, q2, q1, q0) of analytic functions. The originality and potential impact of this research may inspire future investigators to identify new sufficient constraints for functions in the subclass ∁η(q3, q2, q1, q0) across various special functions, particularly hypergeometric, Dini, and Sturve functions.

Suggested Citation

  • Tariq Al-Hawary & Mohamed Illafe & Feras Yousef, 2025. "Certain Constraints for Functions Provided by Touchard Polynomials," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:2581058
    DOI: 10.1155/ijmm/2581058
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    References listed on IDEAS

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    1. Abdulmtalb Hussen & Abdelbaset Zeyani, 2023. "Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials," Mathematics, MDPI, vol. 11(13), pages 1-10, June.
    2. Khristo N. Boyadzhiev, 2009. "Exponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-18, September.
    3. Khristo N. Boyadzhiev, 2009. "Exponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
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