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A bounded linear operator T on a Hilbert space ℋ, satisfying ‖T2h‖2+‖h‖2≥2‖Th‖2 for every h∈ℋ, is called a convex operator. In this paper, we give necessary and sufficient conditions under which a convexcomposition operator on a large class of weighted Hardy spaces is an isometry. Also, we discuss convexity of multiplication operators

On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces