On a class of univalent functions defined by Salagean integro-differential operator

Abstract

In this paper we consider the L n W A ! A, L n f .´/ D .1 / D n f .´/ C I n f .´/ linear operator, where D n is the Sǎlǎgean differential operator and I n is the Sǎlǎgean integral operator. We study several differential subordinations generated by L n. We introduce a class of holomorphic functions L m n .ˇ/, and obtain some subordination results.

New differential subordinations obtained by using a differential-integral Ruscheweyh-Libera operator

“…The new operator is used for obtaining subordination results related to this class. Similar work containing subordination results related to a class of univalent functions obtained by the use of an operator introduced by using a differential operator and an integral one has been published recently [12] and inspired the results shown in this paper. Also, following the same idea, in paper [13], the author introduces new classes obtained by using the linear operator defined with the Sȃlȃgean differential operator and the generalized Alexander operator, studying the characteristics and other properties of these classes and obtaining Fekete-Szegő functional for these classes.…”

“…This theory had a great impact in the field of complex analysis and developed rapidly. Some recent published work can be seen in [7,9,10,[10][11][12].…”

Starlikeness Condition for a New Differential-Integral Operator

“…The idea of combining integral and differential operators is illustrated in the very recent paper [4] where a differential-integral operator was defined and using the method of the subordination chains, differential subordinations in their special Briot-Bouquet form were studied obtaining their best dominant and, as a consequence, criteria containing sufficient conditions for univalence were formulated. Similar work containing subordination results related to a class of univalent functions obtained by the use of an operator introduced by using a differential operator and an integral one can be seen in [5].…”

Sufficient conditions for univalence obtained by using Briot-Bouquet differential subordination

“…A paper containing subordination results related to a class of univalent functions obtained by the use of an operator introduced by using a differential operator and an integral one has been published recently ( [17]) and inspired the results from this paper.…”