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Univalence criteria for a new integral operator. (English) Zbl 1201.30009
Summary: In view of an integral operator ${H}_{{\gamma }_{1},{\gamma }_{2},\cdots ,\gamma |\left[\mathrm{Re}\eta \right]|,\beta ,\eta }$ for an analytic function $f$ in the open unit disk $𝒰$, sufficient conditions for univalence of this integral operator are discussed.

##### MSC:
 30C45 Special classes of univalent and multivalent functions
##### Keywords:
integral operator; univalence; starlike; real part; integer part
##### References:
 [1] Kim, Y. J.; Merkes, E. P.: On an integral of powers of a spirallike function, Kyungpook mathematical journal 12, 249-253 (1972) · Zbl 0252.30017 [2] N.N. Pascu, V. Pescar, On the integral operators of Kim–Merkes and Pfaltzgraff, 32 (55), 2, Mathematica, Univ. Babeş-Bolyai, Cluj-Napoca, 1990, pp. 185–192. · Zbl 0761.30011 [3] Pescar, V.: Univalence conditions for certain integral operators, Journal of inequalities in pure and applied mathematics 7, No. 4 (2006) · Zbl 1131.30320 · doi:emis:journals/JIPAM/article765.html [4] Pescar, V.: Integral operators on a certain class of analytic functions, Libertas Mathematica 27, 95-98 (2007) · Zbl 1138.30011 [5] Pescar, V.; Owa, S.: Univalence problems for integral operators by kim–merkes and pfaltzgraff, Journal of approximation theory and applications 3, No. 1–2, 17-21 (2007) [6] Miller, S. S.; Mocanu, P. T.: Differential subordinations, theory and applications, Monographs and text books in pure and applied mathematics 225 (2000) · Zbl 0954.34003 [7] N.N. Pascu, An improvement of Becker’s univalence criterion, in: Proceedings of the Commemorative Session Simion Stoilow, University of Braşov, 1987, pp. 43–48. · Zbl 0666.30012 [8] Mayer, O.: The functions theory of one variable complex, (1981)