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On Certain Multivalent Functions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 Let𝒮*(p,α)be the class of functionsf(z)which are analytic andp-valently starlike of orderαin the open unit diskE. The object of the present paper is to derive an interesting condition forf(z)to be in the class𝒮*(p,α).
Mamoru Nunokawa +5 more
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Tsukuba Journal of Mathematics, 1991 In this article the authors proved that if p is analytic in the unit disc \(\Delta\), \(p(0)=1\) then \[ (*)\;| p(z)+zp'(z)-1|
Nunokawa, Mamoru +2 more
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Generalized Schur Functions as Multivalent Functions
Complex Analysis and Operator Theory, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multivalent Functions Related with an Integral Operator
International Journal of Mathematics and Mathematical Sciences, 2021 In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close‐to‐convexity, starlikeness, convexity, and Hadamard product.
Syed Ghoos Ali Shah +4 more
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Subclasses of spirallike multivalent functions
Mathematical and Computer Modelling, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nantu Sarkar +2 more
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A class of multivalent functions [PDF]
Transactions of the American Mathematical Society, 1951 This inequality has been proved for n = 2 and n = 3, and for special subclasses of the family of univalent functions (1.2) has been proved for all n. In particular, if all the coefficients in (1.1) are real then (1.2) holds and is sharp for all positive integers n.
Goodman, A. W., Robertson, M. S.
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On multivalent starlike functions [PDF]
Studia Universitatis Babes-Bolyai Matematica, 2019 We prove some new sucient conditions for function to be p-valent, or p-valently starlike in the unit disc.
Mamoru Nunokawa +3 more
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On an Identity Related to Multivalent Functions [PDF]
Proceedings of the American Mathematical Society, 1995 In 1948 A. W. Goodman conjectured that if \(f(z)= \sum_{i=1}^ \infty b_ n z^ n\) is regular and \(p\)-valent in the unit disc \(E= \{z\): \(| z|< 1\}\) then \[ | b_ n|\leq \sum_{k=1}^ p D(p,k, n)| b_ k|, \qquad 1\leq k\leq ...
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A note on multivalent functions [PDF]
Tsukuba Journal of Mathematics, 1989 The author obtained the following lemma: Let \(p(z)\) be analytic in \(| z|
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A note on multivalent functions
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1991 Let \(A_ p(n)\) be the class of functions of the form \(f(z)=z^ p+\sum^ \infty_{k=p+n}a_ kz^ k\) \((p\in \mathbb{N};\;n\in \mathbb{N})\) which are analytic in the open unit disk \(U=\{z:| z|
Sekine, Tadayuki, Owa, Shigeyoshi
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