On the Real Part of a Class of Analytic Functions

  title={On the Real Part of a Class of Analytic Functions},
  author={Basem A. Frasin},
ON THE REAL PART OF A CLASS OF ANALYTIC FUNCTIONS B.A. Frasin Abstract. Let T (β, b), β(β ≥ 0) and b ∈ C denote the class of analytic functions f(z) in the open unit disk which satisfy the condition Re {f ′(z) + βzf ′′(z)} > 1 − |b| . Inclusion relations of functions in the class T (β, b) are given. Lower bounds are also obtained for the n-th partial sums Fn(z) of the Libera integral operator F (z) and the n-th partial sums of f(z). Furthermore, some convolution properties of functions in T… CONTINUE READING

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