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Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Applications of differential subordinations for norm estimates of an integral operator
Part of
- Geometric function theory
Jacek Dziok, Ravinder Krishna Raina, Janusz Sokół
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 2 / April 2018

Published online by Cambridge University Press:

06 November 2017, pp. 281-291

Print publication:

April 2018
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By considering the norm of a locally univalent function given by
we obtain such norm estimates for an operator of functions involving a convolution structure of convex univalent functions with a subclass of convex functions (defined by subordination). We also obtain some inequalities concerning this norm for functions under a certain fractional integral operator. Some implications of our results are briefly pointed out in the concluding section.