New approach to some results related to mixed norm sequence spaces

Abstract

In this paper, the mixed norm sequence spaces ?p,q for 1 ? p,q ? ? are the subject of our research; we establish conditions for an operator T? to be compact, where T? is given by a diagonal matrix. This will be achieved by applying the Hausdorff measure of noncompactness and the theory of BK spaces. This problem was treated and solved in [5, 6], but in a different way, without the application of the theory of infinite matrices and BK spaces. Here, we will present a new approach to the problem. Some of our results are known and others are new. [Projekat Ministarstva nauke Republike Srbije, br. 174007 i br. 174025]

Untitled

“…Thus other variants of l p distance measures can also be used for the clustering. For example, the distance measure of sequence space l p,q , 1 ≤ p, q ≤ ∞ introduced by Kellogg [20] and further studied by Jovanovic and Rakocevic [18], Oscar and Carme [5] and Ivana et al [12] offer more flexibility in comparison to distance measure of l p due to involvement of one more parameter q. In [32], Sencimen and Pehlivan discussed the boundedness of the sequence in probabilistic norm space.…”

A novel sequence space related to L p $\mathcal{L}_{p}$ defined by Orlicz function with application in pattern recognition

“…Clustering is carried out by using other variants of the distance measure. The distance measure of the sequence space , , introduced by Kellogg [ 9 ] and further studied by Jovanovic and Rakocevic [ 10 ], Oscar and Carme [ 11 ], and Ivana et al [ 12 ] offers more flexibility in comparison to due to involvement of additional parameter q . Sargent [ 13 ] introduced another interesting sequence spaces and closely related to .…”