Subclasses of typically-real functions defined by Ruscheweyh derivative

• Autorzy: Lecko A. , Lecko M. , Yaguchi T.
• Języki publikacji: EN

Abstrakty

EN

For each lambda>- 1 let TR(lambda) be the class of all functions f analytic in D= {z is an element of C : \z\ < 1} of the form f (z) = [...] having real coefficients and satisfying the condition [...] where Llambda denote the Ruscheweyh derivative. Some basic properties of functions in are presented.

Słowa kluczowe

EN

univalent function; convex function; Ruscheweyh derivative

PL

funkcje jednolistne; funkcje wypukłe; pochodna Ruscheweyha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 4
• Strony: 823--832
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Lecko A.

autor

Lecko M.

autor

Yaguchi T.

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

Bibliografia

• [1] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446.
• [2] A. W. Goodman, Univalent Functions, Mariner Publishing Co., Tampa, Florida,1983.
• [3] W. E. Kirwan, Extremal problems for the typically real functions, Amer. J. Math. 88 (1966), 942-954.
• [4] Z. Lewandowski, S. Miller, E. Zlotkiewicz, Generating functions for some classes of univalent functions, Proc. Amer. Math. Soc. 56 (1976), 111-117.
• [5] R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965), 755-758.
• [6] M. S. Robertson, On the coefficients of a typically- real functions, Bull. Amer. Math. Soc. 41 (1935), 565-572.
• [7] M. S. Robertson, Analytic functions star-like in one direction, Amer. J. Math. 58 (1936), 465-472.
• [8] M. S. Robertson, Applications of a lemma of Fejer to typically-real functions, Proc. Amer. Math. Soc. 1 (1950), 555-561.
• [9] W. Rogosinski, Uber positive harmonische Entwicklungen und typisch-reelle Potenzreihen, Math. Zeit. 35 (1932), 93-121.
• [10] W. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.