This paper is motivated by the recent progress on the Hermite-Hadamard inequality for convex functions defined on the bounded closed interval, obtained by Z. Pavić [Z. Pavić, Improvements of the Hermite-Hadamard inequality, J. Inequal. Appl. 2015 (2015), Article ID 222]. As a generalization, we obtained a new refinement of the Hermite-Hadamard inequality for co-ordinated convex functions defined on the rectangle.
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In this paper, we will give coefficient conditions for mappings of the form f(z) = z/(1+sum for k=1 bkzk1 to infinity) to be starlike or convex on the Euclidean unit ball B in Cn. Our results give concrete examples of strongly starlike mappings of order a, starlike mappings of order a and convex mappings on B.
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