Kanas, S.; Srivastava, H. M. Linear operators associated with \(k\)-uniformly convex functions. (English) Zbl 0959.30007 Integral Transforms Spec. Funct. 9, No. 2, 121-132 (2000). In terms of the Hadamard product (or convolution), define the operator \(I_{a,b,c}\) by \[ \bigl[I_{a,b,c} (f)\bigr](z) =f(z)*z_2 F_1(a,b;c;z), \] where the function \(f\) is analytic in the unit disk. The classes of \(k\)-uniformly convex and \(k\)-starlike functions \((0\leq k<\infty)\) denoted by \(k\)-UCV and \(k\)-ST, respectively, were introduced recently (see, for example, S. Kanas and A. Wiśniowska [Folia Sci. Univ. Tech. Resoviensis Mat. 22(170), 65-78 (1998)]. The object of the present paper is to find conditions on the parameter \(a,b,c\) and \(k\), for which the linear operator \(I_{a,b,c}\) maps the classes of starlike and univalent functions onto \(k\)-UCV and \(k\)-ST. Reviewer: H.M.Srivastava (Victoria) Cited in 52 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 33E05 Elliptic functions and integrals Keywords:\(k\)-uniformly convex; \(k\)-starlike functions PDF BibTeX XML Cite \textit{S. Kanas} and \textit{H. M. Srivastava}, Integral Transforms Spec. Funct. 9, No. 2, 121--132 (2000; Zbl 0959.30007) Full Text: DOI References: [1] DOI: 10.1007/BF02392821 · Zbl 0573.30014 · doi:10.1007/BF02392821 [2] Hohlov Yu.E., Izv. Vysš. Uč. Zaved. Matematika 10 pp 83– (1978) [3] Kanas S., J. Comput. Appl. Math. 10 (1978) [4] Kanas S., Folia Sci. Univ. Tech. Resoviensis Mat. 22 pp 65– (1998) [5] Kanas S., Rev.Roumanie Math. Pures Appl. 22 (1998) [6] DOI: 10.1090/S0002-9939-1975-0367176-1 · doi:10.1090/S0002-9939-1975-0367176-1 [7] Ruscheweyh S., Convolutions in Geometric Function Theory (1982) · Zbl 0499.30001 [8] Srivastava H.M., Current Topics in Analytic Function Theory (1992) · Zbl 0976.00007 [9] DOI: 10.1080/00207168108803266 · Zbl 0475.33002 · doi:10.1080/00207168108803266 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.