The objective of this study is to identify novel quantum midpoint-type inequalities for twice q-differentiable functions by utilizing Mercer’s approach. We introduce a new auxiliary variant the Mercer identity related functions. By applying theory convex identity, we bounds using well-known inequalities, such as H"older’s inequality and power-mean inequality. provide explicit examples along wit...

An interesting property of the midpoint rule and trapezoidal rule, which is expressed by the so-called Hermite–Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite–Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. I...

Abstract In this paper, we explore a class of Hermite–Hadamard integral inequalities for convex and m -convex functions. The Hölder inequality is used to create class, which has wide range applications in optimization theory. Some trapezoid-type midpoint error estimates are investigated. Inequalities several q -special functions highlighted. As particular cases, have included previous results.

In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals types. Then, prove some new q-midpoint q-trapezoidal estimates for newly established q-Hermite-Hadamard inequality (involving left right proved by Bermudo et al.) under q-differentiable convex functions. Finally, provide examples to illustrate validity obtained inequalities.

In this paper, authors study the concept of (s,m)-exponential type convex functions and their algebraic properties. New generalizations Hermite-Hadamard inequality for function ? products two are proved. Some refinements (H-H) whose first derivative in absolute value at certain power obtain. Finally, many new bounds special means error estimates trapezoidal midpoint formula provided as well.

We discuss Lepp-centroid versus Lepp-midpoint algorithms for Delaunay quality triangulation. We present geometrical results that ensure that the centroid version produces triangulations with both average smallest angles greater than those obtained with the midpoint version and with bigger smallest edges, without suffering from a rare looping case associated to the midpoint method. Empirical stu...

The aim of our study is to establish, for convex functions on an interval, a midpoint version the fractional HHF type inequality. corresponding integral has symmetric weight function composed with increasing as kernel. We also consider identity and establish some related inequalities based this identity. Some special cases can be considered from main results. These results confirm generality at...

We construct a symplectic, globally defined, minimal-variable, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point vortices on a sphere, and the classical Heisenberg spin chain, a spatial discretisation of the Landau–Lifshitz equation. The existence of such an integrator is ...