Characterization of subclasses of univalent functions

• Autorzy: Trojnar-Spelina L.
• Języki publikacji: EN

Abstrakty

EN

We investigate the family of functions f(z) = z +(suma od n=2 do nieskończoności) anzn that are analytic in the unit disk with the property that the domain of values f(z) + 1+ei(alpha):2zf", (alpha is an element of (-pi,pi) is the parabolic region (Imw)2 < 2Rew - 1. Integral representation and convolution characterization are found and some coefficients bounds are given.

Słowa kluczowe

EN

convex functions; starlike functions; uniformly convex functions

PL

funkcje gwiaździste; funkcje wypukłe; funkcje jednostajnie wypukłe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 35--41
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Trojnar-Spelina L.

• Department of Mathematics, Technical University of Rzeszów, W. Pola 2, 35-959 Rzeszów, Poland

Bibliografia

• [1] P. L. Duren, Univalent Functions, Springer-Verlag, New York 1980.
• [2] A. W. Goodman, On uniformly convex functions, Ann. Polon. Math. 56 (1991), 87-92.
• [3] A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991), 364-370.
• [4] S. Kanas, A. Wiśniowska, Conic regions and k-uniform convexity, J. of Comput. and Appl. Math. 105 (1999), 327-336.
• [5] S. Kanas, A. Wiśniowska, Conic regions and k-uniform convexity II, Folia Sci. Univ. Tech. Resov. 22 (1998), 63-75.
• [6] W. Ma, D. Minda, Uniformly convex functions, Ann. Polon. Math. 57 (2)(1992), 165-175.
• [7] W. Ma, D. Minda, Uniformly convex functions II, Ann. Polon. Math. 58 (3) (1993), 275-285.
• [8] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc. 48 (1943), 48-82.
• [9] F. Rønning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. Vol. 118, No 1, May 1993.
• [10] St. Ruscheweyh, Linear operators between classes of prestarlike functions, Comment. Math. Helvetici 52 (1977), 497-509.
• [11] H . Silverman, E. M. Silvia, Characterizations for subclasses of univalent functions, Math. Japonica 50, No. 1 (1999), 103-109.