Growth of entire functions with some univalent Gelfond‐Leontev derivatives

Kapoor, G. P.; Juneja, O. P.; Patel, J.

doi:10.1155/s0161171289000037

Cited by 2 publications

(4 citation statements)

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“…Since series (8) differs from series (7), only that instead l k /l k+1 , it contains (l k /l k+1 ) m , I will easily prove the inequalities…”

Section: Discussionmentioning

confidence: 84%

“…is the usual derivative of the n-th order. The Gelfond-Leont'ev derivative is a very interesting object of investigations (see [6][7][8]). These derivatives found applications in the theory of univalent analytic functions.…”

Section: Introductionmentioning

confidence: 99%

“…These derivatives found applications in the theory of univalent analytic functions. They allows researchers to describe the growth of these functions in other terms [7].…”

Section: Introductionmentioning

confidence: 99%

“…The generalization of the results from [14] to the case of Hadamard compositions of genus m ≥ 1 has become an actual problem. It allows researchers to study the growth properties of these function classes and consider their applications in geometric function theory as it is achieved for usual the Gelfond-Leont'ev derivatives of univalent analytic functions in [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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Hadamard Compositions of Gelfond–Leont’ev Derivatives

Sheremeta

2022

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For analytic functions fj(z)=∑n=0∞an,jzn, 1≤j≤p, the notion of a Hadamard composition (f1*…*fp)m=∑n=0∞∑k1+⋯+kp=mck1…kpan,1k1·…·an,pkpzn of genus m is introduced. The relationship between the growth of the Gelfond–Leont’ev derivative of the Hadamard composition of functions fj and the growth Hadamard composition of Gelfond–Leont’ev derivatives of these functions is studied. We found conditions under which these derivatives and the composition have the same order and a lower order. For the maximal terms of the power expansion of these derivatives, I describe behavior of their ratios.

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“…Since series (8) differs from series (7), only that instead l k /l k+1 , it contains (l k /l k+1 ) m , I will easily prove the inequalities…”

Section: Discussionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

“…These derivatives found applications in the theory of univalent analytic functions. They allows researchers to describe the growth of these functions in other terms [7].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations