Post Quantum Integral Inequalities of Hermite-Hadamard-Type Associated with Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre-Invex Mappings

Abstract

By using the contemporary theory of inequalities, this study is devoted to proposing a number of refinements inequalities for the Hermite-Hadamard’s type inequality and conclude explicit bounds for two new definitions of ( p 1 p 2 , q 1 q 2 ) -differentiable function and ( p 1 p 2 , q 1 q 2 ) -integral for two variables mappings over finite rectangles by using pre-invex set. We have derived a new auxiliary result for ( p 1 p 2 , q 1 q 2 ) -integral. Meanwhile, by using the symmetry of an auxiliary result, it is shown that novel variants of the the Hermite-Hadamard type for ( p 1 p 2 , q 1 q 2 ) -differentiable utilizing new definitions of generalized higher-order strongly pre-invex and quasi-pre-invex mappings. It is to be acknowledged that this research study would develop new possibilities in pre-invex theory, quantum mechanics and special relativity frameworks of varying nature for thorough investigation.

New Post Quantum Analogues of Hermite–Hadamard Type Inequalities for Interval-Valued Convex Functions

“…Recently, Lou et al [8] presented basic properties of Iq-calculus and derived Iq-Hermite-Hadamard inequalities for convex intervalvalued functions. For more details, see [9][10][11][12][13].…”

Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus

“…Tunç and E. Göv [23] presented the (p, q)-derivative and (p, q)-integral on finite intervals in 2016, proved some of their properties, and proved a number of integral inequalities using the (p, q)-calculus. Many researchers have recently begun working in this direction, based on the works of M. Tunç and E. Göv, and some further findings on the analysis of (p, q)-calculus can be found in [24][25][26][27].…”

More new results on integral inequalities for generalized $ \mathcal{K} $-fractional conformable Integral operators

“…However, since in the community of fractional calculus nonlocal fractional derivatives only are used to be called fractional, we prefer to replace conformable fractional by conformable (as a type of local fractional). Conformable derivatives and other types of local fractional derivatives or modified conformable derivatives in [5] can gain their importance by the ability of using them to generate more generalized nonlocal fractional derivatives with singular kernels (see, [1,2,13,15,16,19,21,22,26]).…”

“…Pólya-Szegö types inequalities involving the generalized K-fractional conformable integrals. In this section, we shall derive certain Pólya-Szegö type integral inequalities for real-valued integrable functions via generalized K-fractional conformable integral operator defined in (15). Lemma 2.1.…”

“…3.Cebysev types inequalities involving the generalized K-fractional conformable integrals. In this part, we investigate the left and right generalized K-fractional conformable integrals defined in (15), which generalize the Riemann-Liouville fractional integrals.…”