Close-to-convexity properties of inverse hypergeometric functions

Authors

• IJLAL HUSSAINFollow
• WASIM UL HAQFollow
• JANUSZ SOKOLFollow

Author ORCID Identifier

IJLAL HUSSAIN: 0009-0000-3035-4158

WASIM UL HAQ: 0000-0001-7148-1890

JANUSZ SOKOL: 0000-0003-1204-2286

Abstract

The normalized inverse hypergeometric function zF_ν⁻¹(d, e, f; z) = ∑_s=0^∞ A_sz^s+1 is considered, where A_s = (f)_s(ν + 1)_s / (d)_s(e)_s. We aim to provide constraints on d, e, f, and ν under which zF_ν⁻¹(d, e, f; z) belongs to various subclasses of the class of close-to-convex functions. Coefficient characterizations of these families are derived under additional conditions. Some associated operators are also discussed.

DOI

10.55730/1300-0098.3663

Keywords

Starlike functions, convex functions, close-to-convex functions, hypergeometric functions, inverse hypergeometric functions

First Page

475

Last Page

487

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

HUSSAIN, I, HAQ, W, & SOKOL, J (2026). Close-to-convexity properties of inverse hypergeometric functions. Turkish Journal of Mathematics 50 (3): 475-487. https://doi.org/10.55730/1300-0098.3663