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In this paper the concept of symmetrized convex stochastic processes is introduced. Some characterizations involving Hermite–Hadamard type inequalities and a stability result for symmetrized convex stochastic processes are proved. [ABSTRACT FROM AUTHOR]

In this paper we deal with functions related to generalized convexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend inequalities satisfied by uniformly convex functions, strongly convex functions as well as superquadratic functions. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new class of dynamic inequalities of Hardy's type which generalize and improve some recent results given in the literature. More precisely, we prove some new Hardy-type inequalities involving many functions on time scales. Some new discrete inequalities are deduced in seeking applications. [ABSTRACT FROM AUTHOR]

In this paper, the author discusses a generalization of Schröder's and Abel's functional equation of the form ∑ n α n (x) f (u n (x)) = g (x). In fact, using the theory of operators and infinite matrices, we show under certain conditions this equation has only a unique bounded solution f : X → R. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain Fejér type inequalities for higher order convex functions and the general weighted integral formula involving w-harmonic sequences of functions. Also, Fejér type inequalities are obtained for the general three, four and five point quadrature formulae. Further, Fejér type inequalities for the corrected three, corrected four and corrected five point quadrature formulae are considered. In special cases, Fejér type estimates for Simpson, Maclaurin, corrected Simpson and corrected Maclaurin quadrature rules are derived. [ABSTRACT FROM AUTHOR]

By using superquadracity, the new inequalities in this paper generalize a result of Hardy–Littlewood–Pólya and refine Jensen's type inequalities. Also, inequalities related to rearrangements of sets are obtained. [ABSTRACT FROM AUTHOR]

We use properties of Gegenbauer polynomials to prove that the formula ∑ k = 0 n λ k λ n - k (x + y) 2 k (x - y) 2 n - 2 k = 2 λ n ∑ k = 0 n n k n - λ - 1 / 2 k k - λ - 1 / 2 k x 2 k y 2 n - 2 k (0.1) is valid for all integers n ≥ 0 and complex numbers λ , x , y . The special case λ = - 1 / 2 was proved in 2014 by Gavrea and Ivan. We apply (0.1) and related results to deduce further identities. Among others, we present combinatorial identities involving harmonic numbers and trigonometric functions, and we prove an inequality for a certain cosine sum. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to present essential extensions of results in [7] and [8], and apply them to some special situations. Of particular interest is the refinement of the integral Jensen inequality for vector valued integrable functions. The applications related to four topics, namely f-divergences in information theory (an interesting refinement of the weighted geometric mean–arithmetic mean inequality is obtained as a consequence), norm inequalities, quasi-arithmetic means, Hölder's and Minkowski's inequalities. [ABSTRACT FROM AUTHOR]