Second order differential subordinations and certain subordination relations

• Autorzy: Kowalczyk Joanna
• Języki publikacji: EN

Abstrakty

EN

In the present paper the second order differential subordination (1 - alpha)f(z/z + alphaf'{z) + betazf(z) [...] 1 + Mz \z is an element of U) is investigated. The best dominant of subordination (1) is founded. Connections between subordination (1) and subordination of f(z)/z, f'{z) are given. Further the convexity of the function / satisfying the subordination (1) for special choice of parameters a, alpha, beta and M are derived.

Słowa kluczowe

EN

harmonic functions; convex functions; differential subordination; dominant of the differential subordination

PL

funkcje harmoniczne; funkcje wypukłe; podrzędne różniczkowe

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
• Rocznik: 2002
• Tom: z. 26 [199]
• Strony: 97--106
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kowalczyk Joanna

• University of Rzeszów, Rzeszów, Poland

Bibliografia

• [1] D. J. Hallenbeck, S. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc., 52 (1975), 191-195.
• [2] S. Kanas, J. Stankiewicz, Arithmetic means with reference to convexity condition, Bulletin de la Sociét.
• [3] S. S. Miller, P. T. Mocanu, The theory and applications of second-order differential subordinations, Studia Univ. Babes-Bolyai, Mathematica, XXXIV, 4 (1989), 3-32.
• [4] S. S. Miller, P. T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 2 (1978), 289-305.
• [5] P. T. Mocanu, Same starlikeness condition for analytic functions, Rev. Roumaine Math. Pures Appl., 33 (1988), 117-124.
• [6] P. T. Mocanu, On a starlikeness condition, Mathematica, 35(58) (1993), 175-178.
• [7] S. Ponnusamy, Differential subordinations concerning starlike functions, Proc. of Indian Acad. Sciences, (Math. Sci.), 104 (1994), 397-411.
• [8] S. Ponnusamy, S. Rajasekaran, New sufficient conditions for starlike and univalent functions, J. of Math., 104 (1995).