70 research outputs found
Some Paranormed Difference Sequence Spaces of Order Derived by Generalized Means and Compact Operators
We have introduced a new sequence space
combining by using generalized means and difference operator of order . We
have shown that the space is complete under some
suitable paranorm and it has Schauder basis. Furthermore, the -,
-, - duals of this space is computed and also obtained necessary
and sufficient conditions for some matrix transformations from to . Finally, we obtained some identities or
estimates for the operator norms and the Hausdorff measure of noncompactness of
some matrix operators on the BK space by
applying the Hausdorff measure of noncompactness.Comment: Please withdraw this paper as there are some logical gap in some
results. 20 pages. arXiv admin note: substantial text overlap with
arXiv:1307.5883, arXiv:1307.5817, arXiv:1307.588
Remarkable Applications of Measure of Non-compactness For Infinite System of Differential Equations
The essential goal of our study is to search for a solution of an infinite system of differential equations in two different Banach spaces under certain assumptions by the aid of measure of noncompactness. Also, we establish some interesting examples related to our results
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