The second and third Hankel determinants for starlike and convex functions associated with Three-Leaf function [PDF]
Heliyon, 2023 In this paper, we give sharp bounds of the Hankel determinant H2(3)(f) for the coefficients of functions in the class of starlike functions related to a domain that is like three leaves.
Amina Riaz +3 more
doaj +4 more sources
Selberg integrals and Hankel determinants [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 In our previous works "Pfaffian decomposition and a Pfaffian analogue of $q$-Catalan Hankel determinants'' (by M.Ishikawa, H. Tagawa and J. Zeng, J. Combin. Theory Ser.
Masao Ishikawa, Jiang Zeng
doaj +6 more sources
Hankel determinants, Pad\'e approximations, and irrationality exponents [PDF]
International Mathematics Research Notices, 2015 The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$.
Bugeaud, Yann +3 more
core +6 more sources
Analytic determinants and inverses of Toeplitz and Hankel tridiagonal matrices with perturbed columns [PDF]
Special Matrices, 2020 In this paper, our main attention is paid to calculate the determinants and inverses of two types Toeplitz and Hankel tridiagonal matrices with perturbed columns.
Fu Yaru +3 more
doaj +2 more sources
Hankel determinant for certain new classes of analytic functions associated the activation functions [PDF]
Heliyon, 2023 In this article, we introduce two new classes of analytic functions Jtanh and JSG which are associated with the activation functions and defined by the ratio of analytic representations of convex and starlike functions.
YueJuan Sun +4 more
doaj +2 more sources
Certain inequalities related with Hankel and Toeplitz determinant for q-starlike functions [PDF]
HeliyonIn 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.
Ihtesham Gul +3 more
doaj +2 more sources
Boundary values of Hankel and Toeplitz determinants for q-convex functions [PDF]
MethodsXThe 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
Sarem H. Hadi +5 more
doaj +2 more sources
Third-order Hankel determinant sharp estimates for the inverse of complex valued holomorphic functions [PDF]
HeliyonDetermining coefficient estimates of inverse complex valued function is often more challenging than determining the function itself, leading to a lack of articles on inverse functions by examining sharp estimates of the third-order Hankel determinant ...
Muhammad Abbas +3 more
doaj +2 more sources
Hankel determinants of a Sturmian sequence
AIMS Mathematics, 2021 <abstract><p>Let $ \tau $ be the substitution $ 1\to 101 $ and $ 0\to 1 $ on the alphabet $ \{0, 1\} $. The fixed point of $ \tau $ obtained starting from 1, denoted by $ {\bf{s}} $, is a Sturmian sequence. We first give a characterization of $ {\bf{s}} $ using $ f $-representation.
Haocong Song, Wen Wu
openalex +4 more sources
Estimation of Hankel inequalities of symmetric starlike functions in crescent-shaped domains and their application in image processing [PDF]
Scientific ReportsThis study explores some geometric properties of the class of symmetric starlike functions associated with a Crescent-shaped domain denoted by $$\mathcal {SS}^{*}_{\mathcalligra{cre}}$$ .
Bushra Kanwal +3 more
doaj +2 more sources