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The aim of this paper is to present an analytic characterization of the class of functions convex in the negative direction of the imaginary axis of order (α,β). The method of theproof is based on Julia's lemma

international journal of mathematics and mathematical sciences

The class of functions convex in the negative direction of the imaginary axis of order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$(\alpha, \beta)$"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>β</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>

The class of functions convex in the negative direction of the imaginary axis of order(α,β)