Ann. Polon. Math.

2013

DOI: 10.4064/ap108-1-2

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On classes of uniformly starlike functions

Agnieszka Wiśniowska-Wajnryb¹

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Cited by 5 publications

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“…We have (see ) the following characterization of k ‐uniformly starlike functions in terms of convolution. Theorem Let

f \in S

and

0 \leq k \leq 1

.…”

Section: Resultsmentioning

confidence: 99%

“…If f (z) = ∞ n=0 a n z n and g(z) = ∞ n=0 b n z n then the convolution (or the Hadamard product) of the functions f and g is defined as ( f * g)(z) = ∞ n=0 a n b n z n . We have (see [12]) the following characterization of k-uniformly starlike functions in terms of convolution.…”

Section: Resultsmentioning

confidence: 99%

“…It was proven in that for a fixed

k, 0 \leq k \leq 1,

the class

k − UST

consists of functions from S such that

Re \frac{(z - ζ) f^{'} (z)}{f (z) - f (ζ)} > 0, z \in U, | ζ | \leq k .

…”

Section: Introductionmentioning

confidence: 99%

“…It was proven in [12] that for a fixed k, 0 ≤ k ≤ 1, the class k-UST consists of functions from S such that…”

mentioning

confidence: 99%

See 3 more Smart Citations

The order of starlikeness of the class of uniformly starlike functions

Wiśniowska-Wajnryb

¹

2016

Mathematische Nachrichten

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We investigate classes of k‐uniformly starlike functions which generalize the class UST introduced by Goodman in 1991. Obtained results enable us to solve the problem of finding the largest α≥0 such that the class of k‐uniformly starlike functions is contained in the class of starlike functions of order α.

“…We have (see ) the following characterization of k ‐uniformly starlike functions in terms of convolution. Theorem Let

f \in S

and

0 \leq k \leq 1

.…”

Section: Resultsmentioning

confidence: 99%

“…If f (z) = ∞ n=0 a n z n and g(z) = ∞ n=0 b n z n then the convolution (or the Hadamard product) of the functions f and g is defined as ( f * g)(z) = ∞ n=0 a n b n z n . We have (see [12]) the following characterization of k-uniformly starlike functions in terms of convolution.…”

Section: Resultsmentioning

confidence: 99%

“…It was proven in that for a fixed

k, 0 \leq k \leq 1,

the class

k − UST

consists of functions from S such that

Re \frac{(z - ζ) f^{'} (z)}{f (z) - f (ζ)} > 0, z \in U, | ζ | \leq k .

…”

Section: Introductionmentioning

confidence: 99%

“…It was proven in [12] that for a fixed k, 0 ≤ k ≤ 1, the class k-UST consists of functions from S such that…”

mentioning

confidence: 99%

See 2 more Smart Citations

The order of starlikeness of the class of uniformly starlike functions

Wiśniowska-Wajnryb

¹

2016

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

We investigate classes of k‐uniformly starlike functions which generalize the class UST introduced by Goodman in 1991. Obtained results enable us to solve the problem of finding the largest α≥0 such that the class of k‐uniformly starlike functions is contained in the class of starlike functions of order α.

“…Similarly, the function

h (z) = z / (1 - B z)

is in

scriptUCV

if and only if

| B | \leq 1 / 3

(see ). The class

k - ST

is related to the class

k - UCV

by means of the well‐known Alexander equivalence between the usual classes of convex

scriptCV

and starlike

S^{*}

functions (see also the works , and for further developments involving each of the classes

k - UCV

and

k - ST

).…”

Section: Introductionmentioning

confidence: 99%

On order of strongly starlikeness in the class of uniformly convex functions

²

2015

Mathematische Nachrichten

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In this paper we consider the order of strongly starlikeness in the classes uniformly convex functions.

On a Simple Sufficient Condition for the Uniform Starlikeness

Wiśniowska-Wajnryb

¹

2023

Bull. Malays. Math. Sci. Soc.

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The aim of this paper is to prove the theorem which generates many examples of functions belonging to a geometrically defined class of uniformly starlike functions introduced by Goodman in 1991. Only a very few explicit uniformly starlike functions were known until now. Next we obtain inclusion relations between some subclasses of convex functions and the class of uniformly starlike functions.

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