Some inequalities for interval-valued functions on time scales

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.

Some New Integral Inequalities on Time Scales

By introducing two adjusting parameters, we investigate some new nonlinear integral inequalities on time scales, which provide explicit bounds on unknown functions, and can be used as tools in the qualitative theory of certain classes of dynamic equations on time scales. Mathematics subject classification (2010): 26D15, 26E70.

Some Nonlinear Dynamic Inequalities on Time Scales

Our aim in this paper is to establish some explicit bounds of solutions of a certain class of nonlinear dynamic inequalities on a time scale T which is unbounded above. Also, we establish some sufficient conditions for global existence and an estimate of the rate of decay of the solutions. These on the one hand generalizes and on the other hand furnish a handy tool for the study of qualitative ...

Some Opial-Type Inequalities on Time Scales

and Applied Analysis 3 where r t is positive and continuous function with ∫X a dt/r t < ∞, and if x b 0, then ∫b X |x t |∣∣x′ t ∣∣dt ≤ 1 2 ∫b

Some Pachpatte type inequalities on time scales