Generalizations of Guessab-Schmeisser formula via Fink type identity with applications to quadrature rules

In this work, an expansion of Guessab-Schmeisser two points formula for n-times differentiable functions via Fink type identity is established. Generalization of the main result for harmonic sequence of polynomials is established. Several bounds of the presented results are proved. As applications, some quadrature rules are elaborated and discussed. Error bounds of the presented quadrature rules via Chebyshev-Gruss type inequalities are also provided.