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In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI. The newly developed inequalities are also shown to be extensions of preexisting inequalities in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the fractional Hermite-Hadamard inequality on , where is a set of positive real numbers such that for . Using this inequality, we present a new characterization of convexity of a function defined on . [ABSTRACT FROM AUTHOR]

In this paper, we prove some new dynamic inequalities on time scales whichas special cases contain several generalizations of integral and discreteinequalities due to Hardy, Copson, Leindler, Bennett, Pachpatte and Pečarić and Hanjš. [ABSTRACT FROM AUTHOR]

Let denote the usual class of all normalized functions harmonic and sense-preserving univalent on the unit disk . In this article we show that the set, consisting of those mappings f from for which all Taylor coefficients of the analytic and co-analytic parts of f are integers, consists of only nine functions. The second aim is to discuss the set of those functions which have half-integer coefficients. More precisely, we determine the set of univalent harmonic mappings with half-integer coefficients which are convex in real direction or convex in imaginary direction. This work generalizes the recent paper of Hiranuma and Sugawa. One of the examples generated in this way helps to disprove a conjecture of Bharanedhar and Ponnusamy. [ABSTRACT FROM AUTHOR]

In this paper, some refinements of Hermite-Hadamard type inequalities for GA-convex functions are obtained. Applications of the obtained results to special means are given. [ABSTRACT FROM AUTHOR]

Natural phenomena as well as problems encountered in pure and applied sciences are modeled by ordinary, partial or integral differential equations. Most of these problems have a nonlinear aspect which makes their studies difficult, or even impossible. For this, they must resort to other alternatives; among the methods used is the integral inequalities approach, which allows the study of quantitative and qualitative properties of solutions such as existence, uniqueness, delimitation, oscillation, and stability. In this study, we present some new integral inequalities of the Gronwall–Bellman–Bihari type associated with the fractional derivative of ψ-Hilfer, which represents a strong tool and is applicable in the study of certain differential equations. Several known results are derived and some applications to ordinary differential equations are provided to demonstrate the effectiveness of our finding. [ABSTRACT FROM AUTHOR]

In the present work, we give the definition of an s-convex functions for a convex real-valued function f defined on the set of integers Z. We state and prove the discrete Hermite-Hadamard inequality for s-convex functions by using the basics of discrete calculus (i.e. the calculus onZ). Finally,we state and prove the discrete fractional Hermite-Hadamard inequality for s-convex functions by using the basics of discrete fractional calculus. [ABSTRACT FROM AUTHOR]

Some double integral inequalities of Hermite-Hadamard type for h-convex functions defined on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well. [ABSTRACT FROM AUTHOR]