In this paper we establish the existence of solutions of a more general class of stochastic integral equation of Volterra type. The main tools used here are the measure of noncompactness and the fixed point theorem of Darbo. The results generalize the results of Tsokos and Padgett [9] and Szynal and Wedrychowicz [7]. An application to a stochastic model arising in chemotherapy is discussed.

We study the solvability of the fractional integrodifferential equations of neutral type with infinite delay in a Banach space X. An existence result of mild solutions to such problems is obtained under the conditions in respect of Kuratowski's measure of noncompactness. As an application of the abstract result, we show the existence of solutions for an integrodifferential equation.

We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0, 1]. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in C[0, 1]. The famous Chandrasekhar’s integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

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.

In this paper we present existence theorems for the second order discrete boundary value problem in Banach spaces under weaker conditions we have known. We suppose the weak sequential continuity and some conditions expressed in terms of the measure of weak noncompactness.

In this article, we give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space L1[0,∞). Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.