On a subclass of p-valent functions

• Autorzy: Dziok J.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider a subclass of p-valent functions defined by certain differential-integral operator. By using the Krein-Milman theorem we obtain the extreme points of the classs. Some extremal problems in the class are also determined.

Słowa kluczowe

EN

analytic functions; differential-integral operator; extreme points; Krein-Milman theorem

PL

funkcje analityczne; operator różniczkowo-całkowy; punkty ekstremalne; twierdzenie Krein-Milmana

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 1
• Strony: 63--71
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Dziok J.

• Institute of Mathematics University of Rzeszów ul. Rejtana 16A, PL- 35-310 Rzeszów, Poland,

Bibliografia

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• [2] J. Dziok, Classes of functions defined by certain differential-integral operator, J. Comp. Appl. Math. 105 (1999), 245-255.
• [3] J. Dziok, Some relations including various linear operators, Demonstratio Math. 40 (2007), 77-84.
• [4] Y. C. Kim and H. M. Srivastava, Fractional integral and other linear operators associated with the Gaussian hypergeometric function, Complex Variables Theory Appl. 34 (1997), 293-312.
• [5] D. Hallenbeck and T. H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman Advanced Publishing Program, Boston, Pitman, 1984.
• [6] M. Krein, D. Milman, On the extreme points of regularly convex sets, Studia Math. 9 (1940), 133- 138.
• [7] P. Montel, Sur les families de functions analytiques qui admettent des valeurs exceptionelles dans un domaine, Ann. Sci. Ecole Norm. Sup. 23 (1912), 487-535.
• [8] H. L. Royden, Real Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1988.