Boundary values of Hankel and Toeplitz determinants for q-convex functions

Sarem H. Hadi; Timilehin Gideon Shaba; Zainab S. Madhi; Maslina Darus; Alina Alb Lupaş; Fairouz Tchier

MethodsX (Dec 2024)

Boundary values of Hankel and Toeplitz determinants for q-convex functions

Sarem H. Hadi,
Timilehin Gideon Shaba,
Zainab S. Madhi,
Maslina Darus,
Alina Alb Lupaş,
Fairouz Tchier

Affiliations

Sarem H. Hadi: Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq; Department of Business Management, Al-imam University College, Balad 34011, Iraq; Corresponding author at: Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq.
Timilehin Gideon Shaba: Department of Mathematics, Landmark University, P.M.B., Omu-Aran 1001, Nigeria
Zainab S. Madhi: Department of Mathematics, College of sciences, University of Basrah, Basrah 61001, Iraq
Maslina Darus: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Bangi, Selangor Darul Ehsan 43600, Malaysia
Alina Alb Lupaş: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, Oradea 410087, Romania
Fairouz Tchier: Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia

Journal volume & issue: Vol. 13
p. 102842

Abstract

Read online

The study of holomorphic functions has been recently extended through the application of diverse techniques, among which quantum calculus stands out due to its wide-ranging applications across various scientific disciplines. In this context, we introduce a novel q-differential operator defined via the generalized binomial series, which leads to the derivation of new classes of quantum-convex (q-convex) functions. Several specific instances within these classes were explored in detail. Consequently, the boundary values of the Hankel determinants associated with these functions were analyzed. All graphical representations and computational analyses were performed using Mathematica 12.0. • These classes are defined by utilizing a new q-differential operator. • The coefficient values |ai|(i=2,3,4) are investigated. • Toeplitz determinants, such as the second T2(2) and the third T3(1) order inequalities, are calculated.

Hankel and Toeplitz determinants

Published in MethodsX

ISSN: 2215-0161 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Science
Website: http://www.journals.elsevier.com/methodsx/

About the journal

Abstract

Keywords