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As a continuation of our previous research, we give an estimate of the difference between the weighted arithmetic mean and the geometric one of positive invertible operators.

We explore the role of weighted functional Stolarsky means in providing bounds in generalised Hadamard-type inequalities for g-convex functions. Refinements are given for Levinson's inequality and the generalised Hadamard inequality. Applications are made to multivariate weighted functional Stolarsky means.

A functional generalization is given for Stolarsky mean and its basic properties inves- tigated. Functional means in n variables are also considered.

In this article, all of the cases of the inequality[formula]being or not being valid are discussed for all real numbersx, y ∈ R andx ≠ 0, wherea, b > 0 anda ≠ b. Some recent developments concerning mean values are simply introduced.

A generalization is given of the extension of Hadamard's inequality to r -convex functions. A corresponding generalization of the Fink–Mond–Pecaric inequalities for r -convex functions is established.