Univalence criterion for meromorphic functions and Loewner chains

Abstract

Abstract. The object of the present paper is to obtain a more general condition for univalence of meromorphic functions in the U * . The significant relationships and relevance with other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.

Sufficient conditions for univalence - Univalence of Certain Integral Operators Involving Generalized Struve functions

“…Frasin [18] and Arif and Raza [2] studied the convexity and strongly convexity of the integral operators dened in [4]. Recently Deniz et al [16] and Deniz [10] studied the integral operator dened by generalized Bessel functions of order v. For further details of these univalence criterion, we refer the readers to [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,25,26,27,28]. Motivated by the work of these above authors, we contribute to this univalence theory by studying the univalence of integral operators involving generalized Struve functions.…”

On the univalence of two general integral operators

“…Besides, recently many mathematician have engaged in research of univalence criteria of the integral operators which preserve the class S by aid of well-known lemmas already used in papers on univalence criteria (see, for example, [4-8, 14-17, 27-29, 32, 33]). In terms of different methods, Kanas and Srivastava [18], and Deniz and Orhan [9][10][11] studied univalence criteria for analytic functions defined in U by using the Loewner chains method. Kiryakova, Saigo and Srivastava [20] obtained some univalence criteria for certain generalized fractional integral and derivatives, ancompassing all the linear integro-differential operators.…”