Some sufficient conditions for univalence and close-to-convexity

• Autorzy: Nunokawa Mamoru , Cho Nak Eun , Kwon Oh Sang , Sokół Janusz

Identyfikatory

DOI

10.1515/jaa-2020-2007

• Języki publikacji: EN

Abstrakty

EN

In the class of analytic functions in the unit disc |z| < 1 we prove some new sufficient conditions for functions to be univalent or to be close-to-convex in the unit disc. Also we extend Ozaki’s condition that Re{exp(iα)f ^(p)(z)} > 0 in |z| < 1 implies that f(z) is at most p-valent in |z| < 1.

Słowa kluczowe

EN

analytic functions; univalent functions; Ozaki’s condition

PL

funkcje analityczne; odwzorowanie jednokrotne; warunek Ozaki'ego

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2020
• Tom: Vol. 26, nr 1
• Strony: 91--95
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Nunokawa Mamoru

• University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan

autor

Cho Nak Eun

• Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 608-737, Korea

autor

Kwon Oh Sang

• Department of Mathematics, Kyungsung University, Busan 608-736, Korea

autor

Sokół Janusz

• College of Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland

Bibliografia

• [1] K. Noshiro, On the theory of schlicht functions, J. Fac. Sci. Hokkaido Univ. Jap. 1-2 (1934-1935), 129-135.
• [2] M. Nunokawa and J. Sokół, The univalence of α-project starlike functions, Math. Nachr. 288 (2015), no. 2-3, 327-333.
• [3] M. Nunokawa and J. Sokół, Some simple conditions for univalence, C. R. Math. Acad. Sci. Paris 354 (2016), no. 1, 7-11.
• [4] M. Nunokawa and J. Sokół, New conditions for starlikeness and strongly starlikeness of order alpha, Houston J. Math. 43 (2017), no. 2, 333-344.
• [5] M. Nunokawa, J. Sokół and N. E. Cho, Sufficient conditions for univalence and starlikeness, Bull. Iranian Math. Soc. 42 (2016), no. 4, 933-939.
• [6] S. Ozaki, On the theory of multivalent functions, Sci. Rep. Tokyo Bunrika Daigaku. Sect. A 2 (1935), 167-188.
• [7] S. Ozaki, I. Ono and T. Umezawa, On a general second order derivative, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 5 (1956), 111-114.
• [8] R. Singh and S. Singh, Some sufficient conditions for univalence and starlikeness, Colloq. Math. 47 (1982), no. 2, 309-314.
• [9] T. Umezawa, Analytic functions convex in one direction, J. Math. Soc. Japan 4 (1952), 194-202.
• [10] S. E. Warschawski, On the higher derivatives at the boundary in conformal mapping, Trans. Amer. Math. Soc. 38 (1935), no. 2, 310-340.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).