A class <mml:math alttext="$T_k $" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:math> of analytic functions in the unit disc is defined in which the concept of close-to-convexity is generalized. A necessary condition for a function <mml:math alttext="$f$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math> to belong to <mml:math alttext="$T_k $" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:math>, raduis of convexity problem and a coefficient result are solved in this paper.

International Journal of Mathematics and Mathematical Sciences

On a generalization of close-to-convexity

Abstract

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