TAILIEUCHUNG - Some theorems involving inequalities on p-valent functions

In this paper, some theorems involving inequalities on p-valent functions (that is p-valenty close-to-convex functions, p-valently starlike functions, and p-valently convex functions) are given. Moreover, some applications in the theorems which are important for geometric function theory are also included. | Turk J Math 23 (1999) , 453 – 459. ¨ ITAK ˙ c TUB SOME THEOREMS INVOLVING INEQUALITIES ON P-VALENT FUNCTIONS ¨ H¨ useyin Irmak, Omer Faruk C ¸ etin Abstract In this paper, some theorems involving inequalities on p-valent functions (that is p-valenty close-to-convex functions, p-valently starlike functions, and p-valently convex functions) are given. Moreover, some applications in the theorems which are important for geometric function theory are also included. Keywords: Analytic, p-valent, p-valently colse-to-convex functions, p-valently starlike functions, p-valently convex functions, open unit disk, and Jack’s Lemma. 1. Introduction and Definitions Let T (p) denote the class of functions f(z) of the form f(z) = z p + ∞ X ak z k , (p ∈ N = {1, 2, 3, . . .}), (1) k=p+1 which are analytic and p-valent in the open unit disk U = {z : z ∈ C and

• Toán học
• P valent
• P valently colse to convex functions
• P valently starlike functions
• P valently convex functions
• Open unit disk
• Geometric function
• Geometric sums
• Standard Laplace distribution
• Domain of geometric attraction
• Characteristic function
• Geometrically infinitely divisible
• Geometrically strictly stable
• Radius of uniform convexity
• Mittag Leffler expansions
• Q Bessel functions
• Wright function
• Symmetrization
• Minimal Area Problem
• The hyperbolic metric
• geometric function theory
• Hyperbolic type metrics
• hyperbolic geodesics
• Capacity
• Harmonic measure
• Elementary theory
• The Schiffer variation
• Extremal length
• Loewners method
• probability theory
• Random variable
• Generating function
• Geometric distribution
• Poisson distribution
• Exponential distribution
• Erlang distribution
• Geometric brownian motion
• Gaussian process regression
• Gasoline prices
• Maximum likelihood method
• Covariance function