ON SOME RESULTS OF WEIGHTED HÖLDER TYPE INEQUALITY ON TIME SCALES

A functional generalization of the reverse Hölder integral inequality on time scales

Keywords: Diamond-α integral Time scale Hölder inequality Minkowski's inequality a b s t r a c t In this paper, we establish a functional generalization of the diamond-α integral reverse Hölder inequality on time scales. Some related inequalities are also considered.

Some Results on Weighted Cumulative Entropy

Considering Rao et al. (2004) and Di Crescenzo and Longobardi (2009) studies, Misagh et al. (2011) proposed a weighted information which is based on the cumulative entropy called Weighted Cumulative Entropy (WCE). The above-mentioned model is a Shiftdependent Uncertainty Measure. In this paper, we examine some of the properties of WCE and obtain some bounds for that. In order to ...

Some Complements of Cauchy’s Inequality on Time Scales

To unify the theory of continuous and discrete dynamic systems, in 1990 Hilger [16] proposed the study of dynamic systems on a time scale and developed the calculus for functions on a time scale (i.e., any closed subset of reals). The purpose of this paper is to establish some complements of Cauchy’s inequality on time scales, which extend some results of Cargo [6], Diaz, Goldman, and Metcalf [...

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