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.

The conception of general Lp-mixed width-integral of convex bodies is introduced and related isoperimetric type inequality, Aleksandrov-Fenchel type inequality and a cyclic inequality are established. Further, the extremum values for the general Lpmixed width-integral are obtained. c ©2017 All rights reserved.

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

This paper presents a generalization for systems of partial differential equations of Gronwall's classical integral inequality for ordinary differential equations. The proof is by reducing the vector integral inequality to a vector partial differential inequality and then using a vector generalization of Riemann's method to obtain the final inequality. The final inequality involves a matrix fun...

for all x ∈ [a, b]. This inequality is a connection between the Ostrowski inequality [12] and the Grüss inequality [13]. It can be applied to bound some special mean and some numerical quadrature rules. For other related results on the similar integral inequalities please see the papers [6, 10, 11, 14] and the references therein. The aim of this paper is to extend a generalizations of Ostrowski...

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.

In the present note a general integral inequality is proved in the direction that was initiated by Q. A. Ngô et al [Note on an integral inequality, J. Inequal. Pure and Appl. Math., 7(4) (2006), Art.120].

Sugeno integral was invented a few decades ago as a natural fuzzy analogue of the classical integral Sugeno integral has many interesting applications It is reasonable to expect that it can be used in all application areas where classical integrals are used and in many such areas it is in deed useful Surprisingly however it has never been used in fuzzy control although in traditional control cl...

Sugeno integral was invented a few decades ago as a natural fuzzy-number analogue of the classical integral. Sugeno integral has many interesting applications. It is reasonable to expect that it can be used in all application areas where classical integrals are used, and in many such areas it is indeed useful. Surprisingly, however, it has never been used in fuzzy control, although in tradition...