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Convexity of functions defined by differential inequalities and integral operators

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The convexity conditions for analytic functions defined in the open unit disk satisfying certain second-order and third-order differential inequalities are obtained. As a consequence, conditions for convexity of functions defined by integral operators are also determined.

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Acknowledgments

The authors are grateful to Prof. Dato’ Rosihan M. Ali, Universiti Sains Malaysia, for his valuable comments which improved the presentation of the paper. The authors also thank the referees for their useful comments.

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Correspondence to See Keong Lee.

Additional information

This work was completed while the first author is attached as a postdoctoral fellow at Universiti Sains Malaysia. The research of the third author is supported by the Fundamental Research Grant Scheme (203/PMATHS/6711367).

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Supramaniam, S., Chandrashekar, R., Lee, S.K. et al. Convexity of functions defined by differential inequalities and integral operators. RACSAM 111, 147–157 (2017). https://doi.org/10.1007/s13398-016-0282-6

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  • DOI: https://doi.org/10.1007/s13398-016-0282-6

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