Differential Inequalities and Criteria for Starlike and Univalent Functions

Obradović, Milutin; Ponnusamy, Saminathan; Singh, Vandana; Vasundhra, P.

doi:10.1216/rmjm/1181069500

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…However, until 1 -λ our recent work not much attention has been paid to this class. We have shown that, just like "every normalized (univalent) convex function is starlike of order 1/2", the following analogous result from [9,11] holds,…”

Section: Convolution Theoremsmentioning

confidence: 70%

“…The class U{ 1) ξ U together with its various generalizations and subclasses have been discussed by M. Obradovic and S. Ponnusamy [9] and later by a number of authors (see [10,11,15]). In fact, Krzyz [6] has shown that function in U{λ) admits a Q-quasiconformal extension to the whole complex plane with Q = --γ whenever 0 < Λ < 1.…”

Section: Convolution Theoremsmentioning

confidence: 99%

See 1 more Smart Citation

Two Parameter Families of Close-to-Convex Functions and Convolution Theorems

Barnard¹,

Naik²,

Obradović³

et al. 2004

Analysis

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Using a recently obtained coefficient condition for functions with positive real part by M. Obradovic and S. Ponnusamy. we construct four different useful examples of two parameter families of close-to-convex functions. As a consequence of another well-known coefficient condition due to M. Obradovic and S. Ponnusamy, we obtain a number of results concerning the convolution of two univalent functions. Using these results, we obtain criteria for combinations of hypergeometric functions to be univalent.

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Section: Convolution Theoremsmentioning

confidence: 70%

Section: Convolution Theoremsmentioning

confidence: 99%

Two Parameter Families of Close-to-Convex Functions and Convolution Theorems

Barnard¹,

Naik²,

Obradović³

et al. 2004

Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…In geometric function theory, there has been a great interest among authors in determining the starlikeness or convexity of functions based on di erential subordination and integral operators, see for example [1][2][3][4][5][6][7][8]. In particular, Kanas and Owa [9] studied the convexity of functions by investigating connections between certain second-order di erential subordination and subordination involving expressions of the form f (z)/z, f ′ (z) and + zf ′′ (z)/f ′ (z).…”

Section: Introductionmentioning

confidence: 99%