Natural neighbour co-ordinates (Sibson co-ordinates) is a well-known interpolation scheme for multivariate data tting and smoothing. The numerical implementation of natural neighbour co-ordinates in a Galerkin method is known as the natural element method (NEM). In the natural element method, natural neighbour co-ordinates are used to construct the trial and test functions. Recent studies on NE...

In this paper, we obtain some new Hermite-Hadamard-type inequalities for convex functions on the co-ordinates. We conclude that the results obtained in this work are the refinements of the earlier results.

Abstract In this work, we introduce the notions about Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities co-ordinated convex by applying newly defined integrals. The results of present paper are extension several previously published results.