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Let A be the class of analytic functions f in the open unit disk U = {z : |z| < 1} with the normalization conditions f(0) = f′(0)−1 = 0.
If f(z) = z + P∞ n=2 anzn and > 0 are given, then the T -neighborhood of the function f is defined as TN (f) = ( g(z) = z + ∞X n=2 bnzn 2 A : ∞X n=2 Tn|an − bn| ) , where T = {Tn}∞n=2 is a sequence of positive numbers. In the present paper we investigate some problems concerning T -neighborhoods of functions in various classes of analytic functions with T = ｛ 2−n/n2｝ ∞ n=2. We also find bounds for ∗ T (A,B) defined by ∗ T (A,B) = inf { > 0 : B TN (f) for all f ∈ A} , where A, B are given subsets of A.
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참고문헌 (18)
참고문헌 신청
A. Bielecki / 1962 / Sur une g´en´eralisation de quelques th´eor`emes de M. Biernacki sur les fonctions analytiques / Ann. Polon. Math 12 : 65 ~ 70
F. G. Avkhadiev / 2002 / Convex holes produce lower bound for coefficients / Complex Var. Theory Appl 47 (7) : 553 ~ 563
F. G. Avkhadiev / 2004 / On the coefficients of concave univalent functions / Math. Nachr 271 : 3 ~ 9
F. G. Avkhadiev / 2006 / Sharp inequalities for the coefficients of concave schlicht functions / Comment. Math. Helv 81 (4) : 801 ~ 807
J. Stankiewicz / 1985 / Neighbourhoods of meromorphic functions and Hadamard products / Ann. Polon. Math 46 : 317 ~ 331
F. G. Avkhadiev / 2002 / Convex holes produce lower bound for coefficients / Complex Var. Theory Appl 47 (7) : 553 ~ 563
F. G. Avkhadiev / 2004 / On the coefficients of concave univalent functions / Math. Nachr 271 : 3 ~ 9
F. G. Avkhadiev / 2006 / Sharp inequalities for the coefficients of concave schlicht functions / Comment. Math. Helv 81 (4) : 801 ~ 807
J. Stankiewicz / 1985 / Neighbourhoods of meromorphic functions and Hadamard products / Ann. Polon. Math 46 : 317 ~ 331
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