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Boundary values of Hankel and Toeplitz determinants for -convex functions
Sarem H Hadi1,2, Timilehin Gideon Shaba3, Zainab S Madhi4
1Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq.
Methodsx
|July 29, 2024
Summary
This study introduces new quantum-convex functions using a novel q-differential operator. The research analyzes coefficient properties and boundary values of Hankel and Toeplitz determinants for these quantum calculus functions.
Area of Science:
- Complex Analysis
- Quantum Calculus
- Operator Theory
Background:
- Holomorphic functions are central to complex analysis.
- Quantum calculus offers novel techniques with broad scientific applications.
- Existing research lacks exploration of q-convex functions via generalized binomial series.
Purpose of the Study:
- Introduce a new q-differential operator.
- Define and investigate new classes of quantum-convex (q-convex) functions.
- Analyze coefficient properties and determinant boundary values for these functions.
Main Methods:
- Definition of a novel q-differential operator using the generalized binomial series.
- Derivation of new classes of q-convex functions.
- Calculation of boundary values for Hankel and Toeplitz determinants.
Main Results:
- Successful definition of novel q-convex function classes.
- Detailed exploration of specific function instances.
- Computation of coefficient values and second/third order Hankel and Toeplitz determinant inequalities.
Conclusions:
- The novel q-differential operator effectively generates new classes of q-convex functions.
- The study provides a detailed analysis of the properties of these functions and their associated determinants.
- This work extends the application of quantum calculus in the study of holomorphic functions.
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