DIFFERENTIAL SUBORDINATIONS USING RUSCHEWEYH DERIVATIVE AND SALAGEAN OPERATOR

Yıl 2014, Cilt: 4 Sayı: 1, 33 - 38, 01.06.2014

Alp Lupas Alina

Öz

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

Anahtar Kelimeler

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

Kaynakça

• 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.
• 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.
• D.A. Alb Lupa¸s, Subordinations and Superordinations, Lap Lambert Academic Publishing, 2011.
• S.S. Miller, P.T. Mocanu, Differential Subordinations. Theory and Applications, Marcel Dekker Inc., New York, Basel, 2000.
• St. Ruscheweyh, New criteria for univalent functions, Proc. Amet. Math. Soc., 49(1975), 109-115.
• G. St. S˘al˘agean, Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, Berlin, 1013(1983), 362-372.