Some Hermite–Hadamard type inequalities for geometrically quasi-convex functions

In the paper, we introduce a new concept ‘geometrically quasi-convex function’ and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.     

Some Hermite–Hadamard type inequalities for functions of generalized convex derivative

We obtain some new inequalities of Hermite–Hadamard type. We consider functions that have convex or generalized convex derivative. Additional inequalities are proven for functions whose second derivative in absolute values are convex. Applications of the main results are presented.

     

Hermite–Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces

Some Hermite–Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications in relation with the celebrated Hölder–McCarthy’s inequality for positive operators and Ky Fan’s inequality for real numbers are given as well.     

Hermite–Hadamard type inequalities for the m- and (α, m)-geometrically convex functions

In the paper the authors introduce concepts of the m- and (α, m)-geometrically convex functions and establish some inequalities of Hermite–Hadamard type for these classes of functions.     

New Hermite–Hadamard-type inequalities for convex functions (I)

In this work we establish some new Hermite–Hadamard-type inequalities for convex functions and give several applications for special means.     

Hermite–Hadamard inequality for convex stochastic processes

In this note we extend the classical Hermite–Hadamard inequality to convex stochastic processes.     

Korovkin type theorems and approximate Hermite–Hadamard inequalities

The main results of this paper offer sufficient conditions in order that an approximate lower Hermite–Hadamard type inequality implies an approximate convexity property. The failure of such an implication with constant error term shows that functional error terms should be considered for the inequalities and convexity properties in question. The key for the proof of the main result is a Korovkin type theorem which enables us to deduce the approximate convexity property from the approximate lower Hermite–Hadamard type inequality via an iteration process.     

A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica - We present a tight parametrical Hermite–Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value...     

On fractional stochastic inequalities related to Hermite–Hadamard and Jensen types for convex stochastic processes

Stochastic convexity and its applications are very important in mathematics and probability (Aequationes Mathematicae 20:184–197, 1980). There are two well-known inequalities for convex stochastic processes: Jensen’s inequality and Hermite–Hadamard’s inequality. Recently, Hafiz (Stoch Anal Appl 22:507–523, 2004) has provided fractional calculus for some stochastic processes. The problem is how to formulate these inequalities for stochastic processes in the class of fractional calculus and that is what is done in this paper. Our results generalize the corresponding ones in the literature.     

Ando–Hiai type inequalities for multivariate operator means

ABSTRACT

We present several Ando–Hiai type inequalities for n-variable operator means for positive invertible operators. Ando–Hiai's inequalities given here are not only of the original type but also of the complementary type and of the reverse type involving the generalized Kantorovich constant.     

Fejér and Hermite–Hadamard type results for H-invex functions with applications

Positivity - We investigate the class of H-invex functions including, e.g., the subclasses of convex, c-strongly convex, $$ \varphi $$ -uniformly convex and superquadratic functions. For H-invex...     

On symmetrized stochastic convexity and the inequalities of Hermite–Hadamard type

Aequationes mathematicae - In this paper the concept of symmetrized convex stochastic processes is introduced. Some characterizations involving Hermite–Hadamard type inequalities and a...     

On the $$\mathbb {}$$-Riemann integral and Hermite–Hadamard inequalities for $$\mathbb {}$$-convex functions

In the present paper we introduce a notion of the \(\mathbb {K}\)-Riemann integral as a natural generalization of a usual Riemann integral and study its properties. The aim of this paper is to extend the classical Hermite–Hadamard inequalities to the case when the usual Riemann integral is replaced by the \(\mathbb {K}\)-Riemann integral and the convexity notion is replaced by \(\mathbb {K}\)-convexity.     

Fejér and Hermite–Hadamard type inequalities for <Emphasis Type="Italic">N</Emphasis>-quasiconvex functions

Some new extensions and refinements of Hermite–Hadamard and Fejér type inequalities for functions which are N-quasiconvex are derived and discussed.