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

Abstract

In the present study, two new classes of convex functions are established with the aid of Raina’s function, which is known as the ψ-s-convex and ψ-quasi-convex functions. As a result, some refinements of the Hermite–Hadamard (ℋℋ{\mathcal{ {\mathcal H} {\mathcal H} }})-type inequalities regarding our proposed technique are derived via generalized ψ-quasi-convex and generalized ψ-s-convex functions. Considering an identity, several new inequalities connected to the ℋℋ{\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.

Keywords

• quantum estimates
• hermite–hadamard inequalities
• convex functions
• generalized ψ-convex functions
• raina function