Cesáro partial sums of certain analytic functions
نویسندگان
چکیده
The aim of the present paper is to consider geometric properties such as starlikeness and convexity of the Cesáro partial sums of certain analytic functions in the open unit disk. By using the Cesáro partial sums, we improve some recent results including the radius of convexity. 1 Introduction Let U := {z : |z| < } be a unit disk in the complex plane C and let H denote the space of all analytic functions on U. Here we suppose that H is a topological vector space endowed with the topology of uniform convergence over compact subsets of U. Also, for a ∈ C and n ∈ N, let H[a, n] be the subspace of H consisting of functions of the form f (z) = a + a n z n + a n+ z n+ + · · ·. Further, let A := {f ∈ H : f () = f () – = } and S denote the
منابع مشابه
Partial Sums of Certain Analytic Functions
The object of the present paper is to consider the starlikeness and convexity of partial sums of certain analytic functions in the open unit disk. 2000 Mathematics Subject Classification. Primary 30C45.
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