On Certain Subclasses of Multivalent Analytic Functions with Complex Order Involving a Linear Operator

In the present investigation, we introduce a class 𝓡 p b ( a , c , A , B ) of multivalent analytic functions with complex order, by using a linear operator. For this class, a sufficient condition in terms of the coefficients is obtained, the Fekete–Szegö problem and determination of sharp upper boun...

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Bibliographic Details
Published inVietnam journal of mathematics Vol. 43; no. 3; pp. 645 - 661
Main Authors Sahoo, Ashok Kumar, Patel, Jagannath
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.09.2015
Subjects
Mathematics
Mathematics and Statistics
Saitoh operator
Secondary 33C15
Fekete–Szegö problem
Valent function
Hadamard product
Hankel determinant
Primary 30C45
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Summary:In the present investigation, we introduce a class 𝓡 p b ( a , c , A , B ) of multivalent analytic functions with complex order, by using a linear operator. For this class, a sufficient condition in terms of the coefficients is obtained, the Fekete–Szegö problem and determination of sharp upper bound for the second Hankel determinant is completely solved. We also find the radii of starlikeness and convexity for certain subclass of 𝓡 p b ( a , c , A , B ) . Relevant connections of the results presented here with those obtained in earlier works are pointed out.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-015-0120-8