Certain inequalities related with Hankel and Toeplitz determinant for q-starlike functions
Ihtesham Gul,
Sa'ud Al-Sa'di,
Saqib Hussain,
Saima Noor
Affiliations
Ihtesham Gul
Department of Mathematics, COMSATS University Islamabad, Islamabad, 45550, Pakistan; Government Postgraduate College Mandian, Abbottabad, 22010, Pakistan; Corresponding author.
Sa'ud Al-Sa'di
Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa, 13133, Jordan
Saqib Hussain
Department of Mathematics, COMSATS University Islamabad (Abbottabad Campus), Abbottabad, 22060, Pakistan
Saima Noor
Department of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa, 31982, Saudi Arabia; Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa, 31982, Saudi Arabia
In the present article, we prove the sharp upper bounds for the second order Hankel determinants |H2(1)|,|H2(2)| and related functionals |a2a3−a4|, |a2a5−a3a4| for q-starlike functions. An upper bound for the third order Hankel determinant |H3(1)| along with the sharp upper bounds for Toeplitz determinant |Tm(n)|, where (m,n)∈{(2,2),(2,3),(3,1),(3,2)} are attained. Many known results are also obtained as corollaries of our main results.
