We give a survey of the known results concerning the sets c0(Λ), c(Λ) and c∞(Λ) including their basic topological properties, their first and second dual spaces, and the characterizations of matrix transformations from them into the spaces l∞, c and c0. Furthermore, we establish some new results such as the representations of the general bounded linear operators from c(Λ) into the spaces l∞, c ...

In this paper, we prove some fixed point theorems associated with Tychonoff theorem and measure of noncompactness in the Fr?chet spaces. Moreover, as an application our results, analyze existence solutions for infinite system integral equations Volterra together Hammerstein type. Finally, present example to illustrate effectiveness results.

This paper is concerned with sufficient conditions for the controllability for nonlocal nonlinear impulsivefuzzy stochastic systems in Banach space by using the concept of Mild solution. And the conditions are drive by using Sadovskii fixed point theorem, Hausdorff measure of noncompactness and operator semigroup. 1. Introduction The problem of controllability is to show the existence ofa contr...

In this paper, we present some alternative results concerning with the existence and attractivity dependence of solutions for a class of nonlinear fractional functional differential equations. In our consideration, we apply the well-known Schauder fixed point theorem in conjunction with the technique of measure of noncompactness. Moreover, we provide examples to illustrate the effectiveness of ...

This paper is concerned with a class of partial nonlocal neutral functional differential and integrodifferential equations with bounded delay in Banach spaces, which are more general than those models been studied. Some existence results of mild solutions to such problems are obtained under the conditions in respect of the Hausdorff’s measure of noncompactness.

In this paper, we extend a monotone iterative technique for nonlocal fractional differential equations with finite delay in an ordered Banach space. By using the monotone iterative technique, theory of fractional calculus, semigroup theory and measure of noncompactness, we study the existence and uniqueness of extremal mild solutions. An example is presented to illustrate the main result.

This paper is concerned with semilinear differential equations with nonlocal conditions in Banach spaces. Using the tools involving the measure of noncompactness and fixed point theory, existence of mild solutions is obtained without the assumption of compactness or equicontinuity on the associated linear semigroup.

This article concerns the existence of solutions to nonlocal fractional differential equations in Banach spaces. By using a type of newly-defined measure of noncompactness, we discuss this problem in general Banach spaces without any compactness assumptions to the operator semigroup. Some existence results are obtained when the nonlocal term is compact and when is Lipschitz continuous.