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Abstract: Aichholzer et al. [O. Aichholzer, C. Huemer, S. Kappes, B. Speckmann, C.D. Tóth, Decompositions, partitions, and coverings with convex polygons and pseudo-triangles, Graphs and Combinatorics 23 (2007) 481–507] introduced the notion of pseudo-convex partitioning of planar point sets and proved that the pseudo-convex partition number satisfies . In this paper we prove that , which improves the upper bound on to , thus answering a question posed by Aichholzer et al. in the same paper. [Copyright &y& Elsevier]

Abstract: In this paper we generalize results on convex sequences and convex functions due to Wu and Debnath [S. Wu, L. Debnath, Inequalities for convex sequences and their applications, Comput. Math. Appl. 54 (2007) 525–534] by using some results on similarly separable sequences established in Niezgoda [M. Niezgoda, Remarks on convex functions and separable sequences, Discrete Math. 308 (2008) 1765–1773]. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we extend some recent results on convex functions due to Dragomir [Some majorisation type discrete inequalities for convex functions, Math. Inequal. Appl. 7 (2) (2004) 207–216]. [Copyright &y& Elsevier]

Abstract: Let be a set of points in in general position such that each point is coloured with one of colours. An alternating path of is a simple polygonal whose edges are straight line segments joining pairs of elements of with different colours. In this paper we prove the following: suppose that each colour class has cardinality and is the set of vertices of a convex polygon. Then always has an alternating path with at least elements. Our bound is asymptotically sharp for odd values of . [Copyright &y& Elsevier]