Combinatorial Improvements of Jensen’s Inequality

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Knjiga L. Horvath, K.A. Khan i J. Pečarić, Combinatorial Improvements of Jensen Inequality nastala je iz znanstvenih radova navedenih autora na temu poboljšanja Jensenove nejednakosti. Knjiga je napisana na engleskom jeziku zbog velikog interesa niza svjetskih matematičara. Istraživanja Jensenove nejednakosti intezivna su zato što se radi o najvažnijoj nejednakosti u matematici koja se koristi za definiciju konveksnih funkcija koje se definiraju u raznim područjima matematike.

The present book aims to collect results about refinements of Jensen’s inequality; to provide methods of constructing refinements of Jensen’s inequality, with emphasis on the combinatorial improvements; conformation of old results from new points of view and insights; to define quasi-arithmetic and mixed symmetric means corresponding to the introduced refinements; to generate Cauchy means by using the refinements and the notion of exponential convexity; to study the monotonicity all of these means. The presented overview yields numerous possibilities for further exploration.