Certain inequalities related with Hankel and Toeplitz determinant for q-starlike functions
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View abstract on PubMed
Summary
This summary is machine-generated.This study establishes sharp upper bounds for second-order Hankel determinants and related functionals for q-starlike functions. It also provides an upper bound for the third-order Hankel determinant and sharp upper bounds for Toeplitz determinants.
Area Of Science
- Complex Analysis
- Geometric Function Theory
Background
- The study of analytic functions and their geometric properties is a cornerstone of complex analysis.
- Hankel and Toeplitz determinants are significant in understanding function properties and have applications in various fields.
Purpose Of The Study
- To derive sharp upper bounds for specific Hankel and Toeplitz determinants associated with q-starlike functions.
- To extend existing results and provide new bounds for these important mathematical objects.
Main Methods
- Utilizing techniques from geometric function theory to analyze q-starlike functions.
- Applying methods for calculating and bounding determinantal expressions.
Main Results
- Sharp upper bounds for the second-order Hankel determinants <math></math> and related functionals <math></math>, <math></math> for q-starlike functions.
- An upper bound for the third-order Hankel determinant <math></math> and sharp upper bounds for Toeplitz determinants <math></math> were established.
- The attained nature of these bounds was demonstrated.
Conclusions
- The findings provide precise estimations for Hankel and Toeplitz determinants in the context of q-starlike functions.
- The results generalize and unify several known inequalities in the field.
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