Abstract
In this paper we considered an general integral operator and three classes of univalent functions for which the second order derivative is equal to zero. By imposing supplimentary conditions for these functions we proved some univalent conditions for the considered general operator. Also some interesting particullar results are presented.
Highlights
Let unit disk and let A denote the class of functions f of the form f z z a2z2 a3z3 ¡ ¡ ¡ z â U, 1.1 which are analytic in the open disk U and satisfy the conditions f 0 S {f â A : f are univalent functions in U}
Let A2 be the subclass of A consisting of functions of the form f 0 â1
Let T2 be the subclass of T for which f 0 0
Summary
Let unit disk and let A denote the class of functions f of the form f z z a2z2 a3z3 ¡ ¡ ¡ z â U , 1.1 which are analytic in the open disk U and satisfy the conditions f 0 S {f â A : f are univalent functions in U}. Let T be the univalent subclass of A which satisfies z2f z f z 2 â1 0, c a complex number, |c| ⤠1, c / â 1, and h z z a2z2 ¡ ¡ ¡ a regular function in U. Let the function f z be regular in the disk UR {z â C; |z| < R}, with |f z | < M for fixed M. N, FÎą1,Îą2,...,Îąn,β z becomes the integral operator FÎą,β z considered in 7 When Îąi Îą for all i 1, 2, . . . , n, FÎą1,Îą2,...,Îąn,β z becomes the integral operator FÎą,β z considered in 7
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