Journal
AXIOMS
Volume 12, Issue 8, Pages -Publisher
MDPI
DOI: 10.3390/axioms12080764
Keywords
starlike functions; subordination; Bernoulli's number of second kind; radii problems; inclusion results; coefficient bounds; Hankel determinants
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The aim of this paper is to introduce a class of starlike functions related to Bernoulli's numbers of the second kind. We define phi(BS) ((zeta) over tilde) = ((zeta) over tilde /e((zeta) over tilde) -1)(2) = Sigma(infinity)(n=0) (zeta) over tilde B-n(n)2 /n! , where the coefficients of B-n(2) are Bernoulli numbers of the second kind. We then introduce a subclass of starlike functions F such that (zeta) over tildeF'((zeta) over tilde)/F((zeta) over tilde) (SIC) phi(BS) ((zeta) over tilde). We explore coefficient bounds, radii problems, structural formulas, inclusion relations, and sharp Hankel determinant problems of this class.
The aim of this paper is to introduce a class of starlike functions that are related to Bernoulli's numbers of the second kind. Let phi(BS) ((zeta) over tilde) = ((zeta) over tilde /e((zeta) over tilde) -1)(2) = Sigma(infinity)(n=0) (zeta) over tilde B-n(n)2 /n! , where the coefficients of B-n(2) are Bernoulli numbers of the second kind. Then, we introduce a subclass of starlike functions F such that (zeta) over tildeF'((zeta) over tilde)/F((zeta) over tilde) (SIC) phi(BS) ((zeta) over tilde). found out the coefficient bounds, several radii problems, structural formulas, and inclusion relations. We also found sharp Hankel determinant problems of this class.
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