g. darbo [rend. sem. math. univ. padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. in this paper, we apply the darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.

In this paper, we derive some identities for the Hausdorff measures of noncompactness of certain matrix operators on the sequence spaces X(r,s) of generalized means. Further, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for such operators to be compact. Mathematics subject classification (2010): 46B15, 46B45, 46B50.

In this paper, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for certain matrix operators on the Fibonacci difference sequence spaces `p(F̂ ) and `∞(F̂ ) to be compact, where 1 ≤ p <∞.

We study the existence and stability of solutions for a class of nonlinear functional evolution inclusions involving accretive operators. Our approach is employing the fixed point theory for multivalued maps and using estimates via the Hausdorff measure of noncompactness.

This paper deals with the characterization of compact operators on Ces?ro sequence spaces as an application Hausdorff measure noncompactness. Further, norms certain are investigated.

In this paper, a new class of abstract impulsive Riemann-Liouville fractional partial neutral functional differential equations with infinite delay is introduced. We apply the suitable fixed point theorem together with the Hausdorff measure of noncompactness to investigate the existence of mild solutions for these equations in Banach spaces. Finally, two examples to illustrate the applications ...

In this paper, we give the characterization of some classes of compact operators given by matrices on the normed sequence space , which is a special case of the paranormed Riesz -difference sequence space , . For this purpose, we apply the Hausdorff measure of noncompactness and use some results.