Compactness by the Hausdorff measure of noncompactness

Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers

“…The next lemma [29,Theorem 3.11] gives necessary and sufficient conditions for a matrix transformation from a BK space to 1 to be compact.…”

“…Recently, several authors have studied compact operators on the sequence spaces and given very important results related to the Hausdorff measure of noncompactness of a linear operator. For example [6][7][8][9][10]16,21,26,[29][30][31][32][33][34].…”

Some fixed point results via measure of noncompactness

“…In both theorems the notion of the compactness plays an essential role. On the other hand, the notion of a measure of noncompactness appears in various contexts and played an important role in several branch of mathematics, in particular, nonlinear functional analysis (see, for instance, [3,5,11,13,14]). Consequently, a natural question was appeared: "is it possible to get a fixed point if the compactness is dropped in well-known Schauder fixed point theorem".…”

Multiplication Operators on Cesàro-Orlicz Sequence Spaces

“…For more details on multiplication operators we refer to ( [2], [18], [19], [20], [22], [24]) and refrences therein. Moreover, Compact operators on sequence spaces have recently been studied by Mursaleen and Noman in ( [15], [16]). By B(Ces ϕ (N)) we denote the set of all bounded linear operators from Ces ϕ (N) into itself.…”