Higher order uniformly close-to-convex functions

Khalida Inayat  Noor; Muhammad Aslam  Noor

doi:10.3934/dcdss.2015.8.1277

Article Contents

2015, Volume 8, Issue 6: 1277-1290. Doi: 10.3934/dcdss.2015.8.1277

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Higher order uniformly close-to-convex functions

Khalida Inayat Noor^1, and
Muhammad Aslam Noor^1,

1.
COMSATS Institute of Information Technology, Department of Mathematics, Islamabad

Received: April 30, 2015

Revised: August 31, 2015

Published: November 2015

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Abstract

In this paper, we define and study some subclasses of analytic functions related with $k$-uniformly close-to-convex functions of higher order in the unit disc. These classes unify a number of classes previously studied. The results obtained include rate of growth of coefficients, inclusion relations, radius problems and necessary conditions for univalency. We derive many known results as special cases.

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Mathematics Subject Classification: 30C45, 30A10, 30C50.

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