Results 101 to 110 of about 828 (215)

Second Hankel determinant for bi-starlike and bi-convex functions of order beta

, 2015
In the present investigation the authors obtain upper bounds for the second Hankel determinant H-2(2) of the classes bi-starlike and bi-convex functions of order beta, represented by S-sigma*(beta) and K-sigma(beta), respectively.
ORHAN, Halit, Caglar, Murat, Deniz, Erhan   +2 more
core   +1 more source

On linear systems and τ functions associated with Lamé's equation and Painlevé's equation VI. [PDF]

, 2011
Painleve's transcendental differential equation PVI may be expressed as the consistency condition for a pair of linear differential equations with 2 by 2 matrix coefficients with rational entries.
Gordon Blower, Blower, Gordon
core   +1 more source

On Sharp Estimate of Third Hankel Determinant for a Subclass of Starlike Functions

, 2022
In our present investigation, a subclass of starlike function Sn−1,L* connected with a domain bounded by an epicycloid with n−1 cusps was considered. The main work is to investigate some coefficient inequalities, and second and third Hankel determinants ...
Naseer Alreshidi, Muhammad Arif, Khalil Ullah, Nasser Alreshidi, Lei Shi, Meshal Shutaywi   +5 more
core   +1 more source

Orthogonal polynomials, Catalan numbers, and a general Hankel determinant evaluation

, 2012
In this paper we deal with Hankel determinants of the form det[ai+j+r(x)]i,j=0n, where r is a non-negative integer, an+r(x)=an+r+an+r-1x+⋯+a0xn+r and (an)n⩾0 is a sequence complex numbers.
Marcellán, Francisco, Francisco Marcellán, Chammam, Wathek, Wathek Chammam, Ridha Sfaxi, Sfaxi, Ridha   +5 more
core   +1 more source

Hankel Determinant Structure of the Rational Solutions for Fifth Painlevé Equation [PDF]

, 2013
In this paper, we construct the Hankel determinant representation of the rational solutions for the fifth Painlev\'{e} equation through the Umemura polynomials. Our construction gives an explicit form of the Umemura polynomials $\sigma_{n}$ for $ n\geq 0$
Qusay Soad Abdul-Aziz, Al-Zamil
core  

The Second Hankel Determinant of Logarithmic Coefficients for Strongly Ozaki Close-to-Convex Functions

, 2023
The aim of this paper is to determine sharp bound for the second Hankel determinant of logarithmic coefficients H2 , 1(Ff/ 2) of strongly Ozaki close-to-convex functions in the open unit disk.
Sevtap Sümer Eker, Bilal Şeker, Çekiç, Bilal, Eker, Sevtap Sümer, Şeker, Bilal, Bilal Çekiç, Adam Lecko, Lecko, Adam   +7 more
core   +1 more source

Inverse logarithmic coefficient bounds for starlike functions subordinated to the exponential functions

Journal of Inequalities and Applications
In recent years, many subclasses of univalent functions, directly or not directly related to the exponential functions, have been introduced and studied. In this paper, we consider the class of S e ∗ $\mathcal{S}^{\ast}_{e}$ for which z f ′ ( z ) / f ( z
Lei Shi, Muhammad Abbas, Mohsan Raza, Muhammad Arif, Poom Kumam   +4 more
doaj   +1 more source

Coefficient bounds for certain subclasses of starlike functions

Journal of Inequalities and Applications, 2019
The conjecture proposed by Raina and Sokòł [Hacet. J. Math. Stat. 44(6):1427–1433 (2015)] for a sharp upper bound on the fourth coefficient has been settled in this manuscript. An example is constructed to show that their conjectures for the bound on the
Nak Eun Cho, Virendra Kumar, Oh Sang Kwon, Young Jae Sim   +3 more
doaj   +1 more source

On sharp third Hankel determinant for certain starlike functions

, 2023
In this paper, we provide an estimation for the sharp bound of the third Hankel determinant of starlike functions of order $\alpha$, where $\alpha$ ranges in the interval $[0, 1/6]\cup \{1/2\}$ and thereby extending the result of Rath et al.
Kumar, S. Sivaprasad, Verma, Neha
core  

Hankel Determinants for the Logarithmic Coefficients of a Subclass of Close-to-Star Functions

Journal of Mathematics
Suppose that ST1 is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class ST1 with the determinant entry of logarithmic ...
Dong Guo, Huo Tang, Jun Zhang, Qingbing Xu, Zongtao Li   +4 more
doaj   +1 more source