Inequalities among Eigenvalues of Second-Order Symmetric Equations on Time Scales

Symmetric Rogers-Hölder's inequalities on diamond-α calculus

We present symmetric Rogers--Hölder's inequalities on time scales when $frac{1}{p}+frac{1}{q}+frac{1}{r}=0$ and $frac{r}{p}+frac{r}{q}$ is not necessarily equal to $1$ where $p,$ $q$ and $r$ are nonzero real numbers.

Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions

Some new variants of interval-valued Gronwall type inequalities on time scales

By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.

First order linear fuzzy dynamic equations on time scales

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.

Existence of Solutions to Second-Order BVPs on Time Scales

2 School of Mathematics The University of New South Wales, Sydney NSW 2052, Australia Abstract:We consider a boundary value problem (BVP) for systems of second-order dynamic equations on time scales. Using methods involving dynamic inequalities, we formulate conditions under which all solutions to a certain family of systems of dynamic equations satisfy certain a priori bounds. These results ar...