Abstract. In this paper we consider (2n) -convex functions and completely convex functions. Using Lidstone's interpolating polynomials and conditions on Green's functions we present results for Jensen's inequality and converses of Jensen's inequality for signed measure. By using the obtained inequalities, we produce new exponentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied.Mathematics subject classification (2010): 26D15, 26D20, 26D99.
The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published results is established, and some applications of the extended result are given. Furthermore, Schur-convexity of functions connected to the Hermite-Hadamard inequality is investigated. Finally, some results on convexity and Schur-convexity involving divided difference are considered.
Jensen's inequality induces different forms of functionals which enables refinements for many classic inequalities ([5]). Several refinements of Jensen's inequalities were given in [4]. In this paper we refine Jensen's inequality by separating a discrete domain of it. At the end, we give some applications. (2000): 26D15.
Mathematics subject classification
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