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Geometric properties of a certain general family of integral operators

Srivastava H.M. (University of Victoria, Department of Mathematics and Statistics, Victoria, British Columbia, Canada)
Prajapat J.K. (Central University of Rajasthan, Department of Mathematics, Bandarsindri, Kishangarh, District Ajmer, Rajasthan, India)
Oros Georgia Irina (University of Oradea, Faculty of Sciences, Oradea, România)
Şendruţiu Roxana (University of Oradea, Faculty of Sciences, Oradea, România)

In this paper, we give a set of sufficient conditions for the univalence, starlikeness and convexity of a certain newly-defined general family of integral operators in the open unit disk. Relevant connections of the results presented here with those that were obtained in earlier works as well as several interesting corollaries and consequences of the main results are also presented.

Keywords: Analytic functions, Univalent functions, Integral operators, Starlike functions, Convex functions, Incomplete gamma function, Incomplete Beta function, Gauss hypergeometric function