Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

Mean Value Theorems for Generalized Riemann Derivatives

Let x, e > 0, uo < ... u O be real numbers. Let f be a real valued function and let A (h; u, w)f (x) h-d be a difference quotient associated with a generalized Riemann derivative. Set I = (x + uoh, x + Ud+eh) and let f have its ordinary (d 1)st derivative continuous on the closure of I and its dth ordinary derivative f('I) existent on 1. A necessary and sufficient condition that a ...

Some Weighted Integral Inequalities for Generalized Conformable Fractional Calculus

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.

Multivariable Calculus, Applications and Theory

Some Coding Theorems for Nonadditive Generalized Mean-Value Entropies

We give an optimality characterization of nonadditive generalizedmean-value entropies from suitable nonadditive and generalized mean-value properties of the measure of average length. The results obtained cover many results obtained by other authors as particular cases, as well as the ordinary length due to Shannon 1948. Themain instrument is the l ni function of the word lengths in obtaining t...

Mean Value Theorems on Manifolds

We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as the results of Schoen-Yau, Michael-Simon, etc, on curved Riemannian manifolds. For the heat equation a mean value theorem with respect to ‘heat spheres’ is proved for heat equation with respect to evolving Riemannian metrics via a space-time consideration. Som...