An integral operator on the classes \(\mathcal{S}^{\ast}(\alpha )\) and \(\mathcal{CVH}(\beta )\)

Nicoleta Ularu, Nicoleta Breaz

Abstract


The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order \(\alpha\) and from the class \(\mathcal{CVH}(\beta)\) and also we estimate the first two coefficients for functions obtained by this operator applied on the class \(\mathcal{CVH}(\beta)\).

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References


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Breaz, N., Breaz, D., Acu, M., Some properties for an integral operator on the (mathcal{CVH}(beta))-class , IJOPCA 2 (1) (2010), 53–58.

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Robertson, M. S., Certain classes of starlike functions, Michigan Math. J. 76 (1) (1954), 755–758.

Ularu, N., Convexity properties for an integral operator, Acta Univ. Apulensis Math. Inform. 27 (2011), 115–120.




DOI: http://dx.doi.org/10.2478/v10062-012-0030-0
Date of publication: 2015-07-15 00:00:00
Date of submission: 2016-01-12 12:52:40


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