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A class of superordination-preserving convex integral operator

Saibah Siregar ; School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43 600 Bangi, Selangor, Malaysia
Maslina Darus ; School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43 600 Bangi, Selangor, Malaysia
Teodor Bulboacă ; Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400 084 Cluj-Napoca, Romania


Puni tekst: engleski pdf 213 Kb

str. 379-390

preuzimanja: 674

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Sažetak

If H(U) denotes the space of analytic functions in the unit disk U, for the integral operator Aα,β,γ,δh:KH(U), with KH(U), defined by
Aα,β,γ,δh[f](z)=[β+γzγ0zfα(t)h(t)tδ1dt]1/β,(α,β,γ,δCandhH(U)),
we will determine sufficient conditions on g1, g2, α, β and γ such that
zh(z)[g1(z)z]αzh(z)[f(z)z]αzh(z)[g2(z)z]α
implies
z[Aα,β,γ,δh[g1](z)z]βz[Aα,β,γ,δh[f](z)z]βz[Aα,β,γ,δh[g2](z)z]β.

In addition, both of the subordinations are sharp, since the left-hand side will be the largest function, and the right-hand side will be the smallest function so that the above implication has been held for all f functions satisfying the double differential subordination of the assumption.

The results generalize those of the last author from \cite{bul3}, obtained for the special case α=β and h1.

Ključne riječi

analytic function; starlike and convex function; differential operator; differential subordination

Hrčak ID:

44030

URI

https://hrcak.srce.hr/44030

Datum izdavanja:

9.12.2009.

Posjeta: 1.509 *

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