Some Results for Isotonic Functionals Via an Inequality Due to Kittaneh and Manasrah

Abstract

Abstract. In this paper we obtain some inequalities for isotonic functionals via a reverse and refinement of Young's inequality due to Kittaneh and Manasrah.

Holder-type and Qi-type inequalities for isotonic linear functionals

“…In this section will be given several generalizations of some inequalities from [11] in Theorem 5, 6 and 7 using new Young-type inequality and reverse of Young's inequality given in [1], [7] and [8]. Then a consequence for integral on time scales will be presented.…”

“…Using new generalizations of reverse of Young's inequality given in [7] and [8] will be given new inequalities for isotonic linear functionals starting from some results given in [10].…”

“…The following two generalizations of reversed Holder's inequality for isotonic linear functionals were given in [7] and [8] and will be also used in the next section.…”

Local extreme points and a Young-type inequality

“…New inequalities concerning isotonic linear functionals can be also found in [7], [3], [5], [6] and referinces therein.…”

Several applications for a local Young-type inequality

“…We also need to recall, for the first section, the definition of isotonic linear functional. This definition can be also find in papers as [2], [3], [8], [12] and the references therein. Definition 1.…”