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Let φ be an analytic self-map of open unit disk 픽. A composition operator is defined as (Cφf)(z) = f(φ(z)), for z ∈ 픽and f analytic on 픽. Given an admissible weight w, the weighted Hilbert space Hw consists of all analytic functions f such that ... = |f(0)|² + ∫픽 |f'(z)\²w(z)dA(z) is finite. In this paper, we study composition operators acting between weighted Bergman space Aα² and the weighted Hilbert space Hw. Using generalized Nevalinna counting functions associated with w, we characterize the bounded-ness and compactness of these composition operators. [ABSTRACT FROM AUTHOR]

The study of iterated contraction was initiated by Rheinboldt in 1969. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability. In this paper a brief introduction of iterated contraction maps is given and some fixed point results are discussed. [ABSTRACT FROM AUTHOR]