Abstract In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion $q^{b}$ qb -integral. We prove some new related with right-hand sides -Hermite–Hadamard for differentiable absolute values second derivatives. The results present...

Abstract We establish necessary conditions for the existence of solutions to various systems partial differential inequalities in plane. The obtained provide new Hermite-Hadamard-type differentiable functions In particular, we obtain a refinement an inequality due Dragomir [ On Hadamard’s convex on co-ordinates rectangle from plane , Taiwan. J. Math. 5 (2001), no. 4, 775–788] coordinates.

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.

Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some estimates of Hermite–Hadamard inequalities for integrals. The results presented in paper are generalizations comparable literature on inequalities. Several inequalities, such as midpoint-like inequality, Simpson-like averaged midpoint–trapezoid-like and trapezoid-like obtained special cases ...

The main objective of this paper is to establish some new variants the Jensen–Mercer inequality via harmonically strongly convex function. We also propose fractional analogues Hermite–Hadamard–Jensen–Mercer-like inequalities using AB integrals. In order obtain our results, we derive integral identities. To demonstrate significance present interesting applications special means and error bounds ...

The main goal of this work is to provide quantum parametrized Hermite-Hadamard like type integral inequalities for functions whose second derivatives in absolute values follow different convexities. A new identity derived twice differentiable functions, which used as a key element our demonstrations along with several basic such as: power mean inequality, and Holder’s inequality. symmetry the s...

We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follow...

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.