EXTENSIONS FOR CERTAIN SUBORDINATION RELATIONS

Yıl 2014, Cilt: 4 Sayı: 1, 56 - 61, 01.06.2014

Kazuo Kuroki

Öz

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.

Anahtar Kelimeler

Analytic function, Univalent function, Integral operator, Subordination

Kaynakça

• 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.