Browsing by Author "Kumar, Sushil"

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    Bound on Hankel Determinants H(2)4 (F) and H(3)4 (F) for Lemniscate Starlike Functions
    (Honam Mathematical Soc., 2023) Kumar, Sushil; Rai, Pratima; ÇETİNKAYA, ASENA
    We determine the upper bounds on fourth order Hankel de-terminants H4(2) (f) and H(3) 4 (f) for the class S*L of lemniscate starlike functions defined on the open unit disk which was introduced by Sok ' o l and Stankiewicz in [17].
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    Coefficient Inequalities for Certain Starlike and Convex Functions
    (Hacettepe University, 2022) ÇETİNKAYA, ASENA; Kumar, Sushil
    In this paper, we consider two Ma-Minda-type subclasses of starlike and convex functions associated with the normalized analytic function phi(Ne)(z) = 1 + z - z3/3 that maps an open unit disk onto the Nephroid shaped bounded domain in the right-half of the complex plane. We investigate convolution and quasi-Hadamard product properties for the functions belonging to such classes. In addition, we compute best possible estimates on third order Hermitian-To eplitz determinant and non-sharp estimates on certain third order Hankel determinants for the starlike functions associated with the interior region of Nephroid.
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    Geometric Properties of Starlikeness Involving Hyperbolic Cosine Function
    (Korean Mathematical Society, 2024) Ahuja, Om P.; ÇETİNKAYA, ASENA; Kumar, Sushil
    In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, BriotBouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.
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    Hankel Determinants of Normalized Analytic Functions Associated with Hyperbolic Secant Function
    (Multidisciplinary Digital Publishing Institute (MDPI), 2024) Kumar, Sushil; Breaz, Daniel; Cotirla, Luminita-Ioana; ÇETİNKAYA, ASENA
    In this paper, we consider a subclass of normalized analytic functions associated with the hyperbolic secant function. We compute the sharp bounds on third- and fourth-order Hermitian–Toeplitz determinants for functions in this class. Moreover, we determine the bounds on second- and third-order Hankel determinants, as well as on the generalized Zalcman conjecture. We examine a Briot–Bouquet-type differential subordination involving the Bernardi integral operator. Finally, we obtain a univalent solution to the Briot–Bouquet differential equation, and discuss the majorization property for such function classes. © 2024 by the authors.
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    Univalent Functions Associated with the Symmetric Points and Cardioid-shaped Domain Involving (p,q)-Calculus
    (Kyungpook Natl Univ, Dept Mathematics, 2021) Ahuja, Om; Bohra, Nisha; ÇETİNKAYA, ASENA; Kumar, Sushil
    In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p,q)-Fekete-Szego inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.