UPPER BOUND FOR THIRD HANKEL DETERMINANT OF A CLASS OF ANALYTIC FUNCTIONS

We establish upper bounds for second Hankel determinant, the Fekete-Szego functional and third Hankel determinant for normalized analytic functions f [member of] [W.sub.[beta]] ([alpha], [gamma]), [W.sub.[beta]]([alpha],[gamma]) = {f: Re ((1-[alpha]+2[gamma])f(z)/z+([alpha]-2[gamma])f'(z)+[gamm...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 4; p. 1472
Main Authors Verma, S, Kumar, R, Murugusundaramoorthy, G
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.09.2023
Elman Hasanoglu
Subjects
Analytic functions
Functional equations
Functions
Inequalities (Mathematics)
Mathematics
Matrices
Upper bounds
India
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ISSN2146-1147
2146-1147

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Summary:We establish upper bounds for second Hankel determinant, the Fekete-Szego functional and third Hankel determinant for normalized analytic functions f [member of] [W.sub.[beta]] ([alpha], [gamma]), [W.sub.[beta]]([alpha],[gamma]) = {f: Re ((1-[alpha]+2[gamma])f(z)/z+([alpha]-2[gamma])f'(z)+[gamma]zf"(z) > [beta]}, where [alpha], [gamma] [greater than or equal to] 0 and [beta] < 1. Also, we show that these bounds reduce to the bounds of some well-known classes for particular choices of parameters [alpha], [gamma] and [beta]. Keywords: Analytic functions, Coefficient inequalities, Hankel determinant, Fekete-Szego. AMS Subject Classification: 30C45, 30C50.
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ISSN:2146-1147
2146-1147