a b s t r a c tIn this paper, we obtain an Ostrowski and Ostrowski-Grüss type inequality on time scales, which not only provides a generalization of the known results on time scales, but also give some other interesting inequalities as special cases.
Abstract. In this paper we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski, trapezoid and Grüss type inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases.Mathematics subject classification (2010): Primary 26D15, 26E70.
In this article, we study the reverse Hölder type inequality and Hölder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using Hölder inequalities on time scales which give Hardy's inequalities as spacial cases.
Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.
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