General Opial Type Inequality for Quotient of Functions - Barbir, Ana; Kruli´c Himmelreich, Kristina; Peˇčarić, Josip (Sarajevo Journal of Mathematics, 2024)
In this paper we give the general Opial type inequality for quotient of functions. Our result contains two functions, convex and concave functions. We prove a new general inequality on a measure space $(Ω,Σ,μ)$. We apply our result to numerous symmetric functions and obtain new results that involve Green's functions, Lidstone series and the Hermite's interpolating polynomials.