Original scientific paper

Univalence criteria for linear fractional differential operators associated with a generalized Bessel function

Huda M Al-Kharsani ; Department of Mathematics, College of Sciences, University of Dammam, 838 Dammam, Saudi Arabia
Abeer M Al-Zahrani ; Department of Mathematics, College of Sciences, University of Dammam, 838 Dammam, Saudi Arabia
Sumaya S Al-Hajri ; Department of Mathematics, College of Sciences, University of Dammam, 838 Dammam, Saudi Arabia
Tibor K Pogany ; Faculty of Maritime Studies, University of Rijeka, Rijeka, Croatia

Abstract

In this paper our aim is to establish some generalizations upon the sufficient conditions for linear fractional differential operators involving the normalized forms of the generalized Bessel functions of the first kind to be univalent in the open unit disk as investigated recently by [{\sc E. Deniz, H. Orhan, H.M. Srivastava}, {\it Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions}, Taiwanese J. Math. {\bf 15} (2011), No. 2, 883-917] and [{\sc \'A. Baricz, B. Frasin}, {\it Univalence of integral operators involving Bessel functions}, Appl. Math. Letters {\bf 23} (2010), No. 4, 371--376]. Our method uses certain Luke's bounding inequalities for hypergeometric functions ${}_{p+1}F_p$ and ${}_pF_p$.

Keywords

Analytic functions; Univalent functions; Integral operator; Generalized Bessel functions; Ahlfors-Becker univalence criteria; Fractional dierential operator; Generalized hypergeometric functions; Luke's bounds

Hrčak ID:

170382

URI

https://hrcak.srce.hr/170382

Publication date:

11.11.2016.

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