Kazuo KUROKİ

EXTENSIONS FOR CERTAIN SUBORDINATION RELATIONS

ISSN: 2146-1147
Başlangıç: 2010
Yayıncı: Turkic World Mathematical Society

For some complex number γ which has a positive real part, a certain subordination relation concerned with the Bernardi integral operator Iγ was proven by D. J. Hallenbeck and St. Ruscheweyh Proc. Amer. Math. Soc. 52 1975 , 191-195 . By considering the analyticity of the functions defined by the Bernardi integral operator Iγ for some non-zero complex number γ with Re γ ≤ 0, an extension for certain subordination relation are discussed.

Keywords:

Analytic function, Univalent function, Integral operator Subordination,

PDF

___

Alexander, J. W., (1915), Functions which map the interior of the unit circle upon simple regions, Ann. of Math., 17, 12-22.
Bernardi, S. D., (1983), Bibliography of Schlicht Functions, Mariner Publishing Company, Tampa, Florida.
Hallenbeck, D. J. and Ruscheweyh, St., (1975), Subordination by convex functions, Proc. Amer. Math. Soc., 52, 191-195.
Kuroki, K. and Owa, S., On the univalence conditions for certain class of analytic functions, Hokkaido Math. J., in press.
Kuroki, K. and Owa, S., Notes on the open door lemma, Rendiconti del Seminario Matematico della Universit`a di Padova., accepted.
Miller, S. S. and Mocanu, P. T., (2000), Diﬀerential Subordinations, Pure and Applied Mathematics, 225, Marcel Dekker.