On some inequalities for uniformly convex mapping with estimations to normal distributions

Abstract

Abstract In this paper, we introduce notable Jensen–Mercer inequality for a general class of convex functions, namely uniformly convex functions. We explore some interesting properties of such a class of functions along with some examples. As a result, we establish Hermite–Jensen–Mercer inequalities pertaining uniformly convex functions by considering the class of fractional integral operators. Moreover, we establish Mercer–Ostrowski inequalities for conformable integral operator via differentiable uniformly convex functions. Finally, we apply our inequalities to get estimations for normal probability distributions (Gaussian distributions).

Keywords

• Hermite–Mercer inequality
• Uniformly convex functions
• Integral inequalities
• Fractional integrals