DIFFERENTIAL SUBORDINATIONS USING RUSCHEWEYH DERIVATIVE AND SALAGEAN OPERATOR

Abstract

In the present paper we study the operator defined by using the Ruscheweyh derivative R mf z and the S˘al˘agean operator S mf z , denoted L m α : An → An, Lm α f z = 1−α R mf z +αSmf z , z ∈ U, where An = {f ∈ H U : f z = z+an+1z n+1+. . . , z ∈ U} is the class of normalized analytic functions. We obtain several differential subordinations regarding the operator L m α

Keywords

• differential subordination,convex function,best dominant,differential operator,S˘al˘agean operator,Ruscheweyh derivative

References

1. A. Alb Lupa¸s, On special differential subordinations using S˘al˘agean and Ruscheweyh operators, Math- ematical Inequalities and Applications, Volume 12, Issue 4, 2009, 781-790.
2. A. Alb Lupa¸s, D. Breaz, On special differential superordinations using S˘al˘agean and Ruscheweyh op- erators, Geometric Function Theory and Applications’ 2010 (Proc. of International Symposium, SoŞa, 27-31 August 2010), 98-103.
3. D.A. Alb Lupa¸s, Subordinations and Superordinations, Lap Lambert Academic Publishing, 2011.
4. S.S. Miller, P.T. Mocanu, Differential Subordinations. Theory and Applications, Marcel Dekker Inc., New York, Basel, 2000.
5. St. Ruscheweyh, New criteria for univalent functions, Proc. Amet. Math. Soc., 49(1975), 109-115.
6. G. St. S˘al˘agean, Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, Berlin, 1013(1983), 362-372.