On the coefficients of meromorphic schlicht functions

Nehari, Zeev; Netanyahu, E.

doi:10.1090/s0002-9939-1957-0083038-0

Cited by 34 publications

(13 citation statements)

References 4 publications

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“…The above lemma is equivalent to a lemma of Nehari and Netanyahu [7]. The following lemma is a simple consequence of the above lemma.…”

Section: Recently Mocanumentioning

confidence: 75%

New Subclasses of the Class of Close-to-Convex Functions

Chichra¹

1977

Proceedings of the American Mathematical Society

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Abstract.In this paper we introduce new subclasses of the class of closeto-convex functions. We call a regular function yfz) an alpha-close-to-convex function if (f(z)f'(z)/z) ¥= 0 for z in E and if for some nonnegative real number a there exists a starlike function a>(z) = z + ■■ • such that Rer(1_a)cí£) + a(£ñf]>0 for z in E.We have proved that all alpha-close-to-convex functions are close-toconvex and have obtained a few coefficient inequalities for a-close-to-convex functions and an integral formula for constructing these functions.Let ?a be the class of regular and normalised functions j(z) which satisfy Re (f'(z) + 0 for z in E.f(z) e % gives Re/'(z) > 0 for z in E provided Rea > 0. A sharp radius of uni valence of the class of functions fiz) for which zf'(z) e 9tt has also been obtained.

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“…The above lemma is equivalent to a lemma of Nehari and Netanyahu [7]. The following lemma is a simple consequence of the above lemma.…”

Section: Recently Mocanumentioning

confidence: 75%

New Subclasses of the Class of Close-to-Convex Functions

Chichra¹

1977

Proceedings of the American Mathematical Society

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“…where the subclass Ω ( ) was introduced and studied by Wang et al [1] and Nehari and Netanyahu [2]. A -hypergeometric function is a power series in one complex variable with power series coefficients which depend (apart from ) on complex upper parameters , , ( = 1, .…”

Section: Introductionmentioning

confidence: 99%

Some Properties for an Integral Operator Defined by Generalized Hypergeometric Function

Aldawish

Darus

2014

Journal of Applied Mathematics

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“…For f Σ, Wang et al [1] and Nehari and Netanyahu [2] introduced and studied the subclass Σ N (b) of Σ consisting of functions f(z) satisfying − zf (z) f (z) + 1 < β (β > 1, z ∈ U).…”

Section: Introductionmentioning

confidence: 99%