Ostrowski like inequalities for ( α , β , γ , δ ) -convex functions via fuzzy Riemann integrals
Abstract
In this paper, we present first time the generalised notion of \((\alpha,\beta,\gamma,\delta)\)-convex (concave) functions in mixed kind, which is the generalisation of functions: convex (concave), \(P\)-convex (concave), quasi-convex (concave), \(s\)-convex (concave) in \(1^{\rm st}\) kind, \(s\)-convex (concave) in \(2^{\rm nd}\) kind, \((s,r)\)-convex (concave) in mixed kind, \((\alpha,\beta)\)-convex (concave) in \(1^{\rm st}\) kind, \((\alpha,\beta)\)-convex (concave) in \(2^{\rm nd}\) kind. Our aim is to establish Ostrowski like inequalities via fuzzy Riemann integrals for \((\alpha,\beta,\gamma,\delta)\)-convex functions in mixed kind by applying several techniques involving power mean inequality and Hölder's inequality. Moreover, we would obtain various consequences with respect to the convexity of function as corollaries and remarks.