New quantum integral inequalities for some new classes of generalizedψ-convex functions and their scope in physical systems

Abstract

AbstractIn the present study, two new classes of convex functions are established with the aid of Raina’s function, which is known as theψ-s-convex andψ-quasi-convex functions. As a result, some refinements of the Hermite–Hadamard ({\mathcal{ {\mathcal H} {\mathcal H} }})-type inequalities regarding our proposed technique are derived via generalizedψ-quasi-convex and generalizedψ-s-convex functions. Considering an identity, several new inequalities connected to the{\mathcal{ {\mathcal H} {\mathcal H} }}type for twice differentiable functions for the aforesaid classes are derived. The consequences elaborated here, being very broad, are figured out to be dedicated to recapturing some known results. Appropriate links of the numerous outcomes apprehended here with those connecting comparatively with classical quasi-convex functions are also specified. Finally, the proposed study also allows the description of a process analogous to the initial and final condition description used by quantum mechanics and special relativity theory.