Some New Generalizations of Reverse Hilbert-Type Inequalities 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.

On reverse Hilbert-type inequalities

*Correspondence: [email protected] 1School of Mathematical Science, Huaibei Normal University, Huaibei, 235000, P.R. China Full list of author information is available at the end of the article Abstract By introducing two pairs of conjugate exponents and estimating the weight coefficients, we establish reverse versions of Hilbert-type inequalities, as described by Jin (J. Math. Anal. Appl. 340:...

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

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.