Recommended by Elena BravermanThis article analyses the asymptotic behaviour of solutions of linear Volterra difference equations. Some sufficient conditions are presented under which the solutions to a general linear equation converge to limits, which are given by a limit formula. This result is then used to obtain the exact asymptotic representation of the solutions of a class of convolution scalar difference equations, which have real characteristic roots. We give examples showing the accuracy of our results.
Abstract.We give a refinement of the discrete Jensen's inequality in the convex and mid-convex cases. For mid-convex functions our result is a common generalization of known inequalities. We illustrate the scope of the results by applying them to some special situations.Mathematics subject classification (2010): 26D07 (26A51).
Abstract. Refinements of the operator Jensen inequality for convex and operator convex functions are given by using cyclic refinements of the discrete Jensen inequality. Similar refinements are fairly rare in the literature. Some applications of the results to norm inequalities, to the Hölder-McCarthy inequality and to generalized weighted power means for operators are presented.
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