On a problem H. S. Al-Amiri and M. O. Reade

• Autorzy: Singh S. , Gupta S.
• Języki publikacji: EN

Abstrakty

EN

In the present paper, the authors investigate the univalence of the functions f, analytic in -E, f(O) = 0, f'(0) = 1 and which satisfy Re [(1 - alfa)f'(z) + alfa (1+ zf''(z): f'(z)] >beta, z is an element of E, where alfa > 0 and 0 < beta < 1. The univalence of such functions has already been established in the case when alfa < 0 and beta = 0 by H. S. Al-Amiri and M. 0. Reade in 1975.

Słowa kluczowe

EN

univalent functions; starlike functions; differential subordination

PL

funkcje uniwalentne; funkcje gwiaździste; podrzędne różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 303--311
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Singh S.

• Sant Longowal Institute of Engineering and Technology, Longowal-148106 (Punjab) - India

autor

Gupta S.

• Sant Longowal Institute of Engineering and Technology, Longowal-148106 (Punjab) - India

Bibliografia

• [1] M. Abramowitz, I. A. Stegun, Hand Book of Mathematical Functions, Dover Publications Inc., New York (1971).
• [2] O. P. Ahuja, H. Silverman, Classes of functions whose derivatives have positive real part, J. Math. Anal. Appl. 138, No. 2 (1998), 385-392.
• [3] H. S. Al-Amiri and M. O. Reade, On a Linear combination of some expressions in the theory of univalent functions, Monatsh. Math. 80, (1975), 257-264.
• [4] P. Eenigenburg, S. S. Miller, P. T. Mocanu, M. O. Reade, On a Briot-Bouquet differential subordination, General Inequalities 3 (1983), (Birkhauser-Verlag, Basel), 339-348.
• [5] S. S. Miller, Differential inequalities and Carathéodory functions, Bull. Amer. Math. Soc. 81(1975) , 79-81.
• [6] S. S. Miller and P. T. Mocanu, Differential Subordinations-Theory and Applications, Marcel Dekker Inc., New York, Basel (2000).
• [7] S. S. Miller, P. T. Mocanu, M. O. Reade, All α-convex functions are univalent and starlike, Proc. Amer. Math. Soc. 37 (1973), 553-554.
• [8] S. S . Miller, P. T. Mocanu, M. O. Reade, Barilevič functions and generalized convexity, Rev. Roumaine Math. Pures Appl. 19 (1974), 213-224.
• [9] P. T. Mocanu , Some integral operators and starlike functions, Rev. Roumaine Math. Pures Appl., 31(1986) 231-235.
• [10] K. Noshiro, On the theory of schlicht functions, J. Fac. Sci. Hokkaido Univ . 2 (1934-35), 129-155.
• [11] S. E. Warchawski, On the higher derivatives at the boundary in conformal mappings, Trans. Amer. Math. Soc. 38 (1935), 310-340.
• [12] D. Wilken and J. Feng, A remark on convex and starlike functions, J. London Math. Soc. (2) 21 (1980) 287-290.