The compact operators on the Riesz sequence space 1 ∞ have been studied by Başarır and Kara, “IJST (2011) A4, 279-285”. In the present paper, we will characterize some classes of compact operators on the normed Riesz sequence spaces and by using the Hausdorff measure of noncompactness.

In this paper we present an existence result for causal functional evolution equations. The result is obtained under a condition with respect to the Hausdorff measure of noncompactness. An application with partial differential equations is given to illustrate our main result. Mathematics subject classification (2010): 34A07, 34A08.

We provide a natural topology for a cone metric space and a noncompactness measure is defined for this space, which enables us to extend existing results for mappings and set-valued mappings defined on classical metric spaces. Moreover it is proved that the topology of any uniform topological space is generated by a cone metric. c ©2016 All rights reserved.

The principal goal of this work is to solvability the mild solution for second‐order hyperbolic PDE with initial/boundary‐value problem nonlocal condition form where open. Our analysis relies on technique measure noncompactness.

In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.