X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius.

In this paper we extend some estimates of the right hand side of a Hermite-Hadamard type inequality for the product two differentiable functions whose derivatives absolute values are convex. Some natural applications to special weighted means of real numbers are given. Finally, an error estimate for the Simpson’s formula is also addressed.

The results obtained in this paper are a correction of the main results obtained in [14], for which we also give an alternative proof and improvement. We also study some new monotonic conditions under which various generalizations of the Hermite-Hadamard inequality are valid. Furthermore, we give an improvement of the obtained results. Mathematics subject classification (2010): 26A48, 26A51, 26...

In this paper, we establish several weighted inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works. Mathematics Subject Classification (2010): 26D15.

We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly h-convex functions. Finally, a Hermite–Hadamard–type inequality for strongly h-convex functions is given.

Abstract The Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from research point view. Currently, mathematicians are working on extending, improving, and generalizing this inequality. This article presents conticrete Hermite-Hadamard-Jensen-Mercer type in weighted unweighted forms by using idea majorization convexity together with generalized conformable fracti...

In this work, we address and explore the concept of generalized \(m\)-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate current initiated idea. Furthermore, prove latest variant Hermite-Hadamard type inequality employing proposed definition preinvexity. We also derive severa...

The Hermite-Hadamard inequality has been recognized as the most pivotal which grabbed attention of several mathematicians. In recent years, load results have established for this inequality. main theme article is to present generalized via Jensen-Mercer and majorization concept. We establish a type majorized tuples. With aid weighted Mercer?s inequality, we also prove certain idea obtaining pap...