On a measure of noncompactness in the space of functions with tempered increments

An extension of Darbo's theorem and its application to system of neutral differential equations with deviating argument

“…Darbo's fixed point theorem [7] which ensures the existence of fixed point is an important application of this measure, since it generalizes both Schauder fixed point and Banach contraction principle. Thereafter, many investigations and papers have been appeared in the MNC and it's application, see for example [1,2,5,8,10]. The aim of this paper is to generalize the Darbo's fixed point theorem via the concept of the class of operators O.f I :/ and extend the results of the theorem presented by Samadi and Ghaemi in [10].…”

Applications of measure of noncompactness to coupled fixed points and systems of integral equations

“…For x 2 BC.R C / the norm of x is defined by k x kD supfjx.t /j W t 0g. Now, we reacal the definition of measure of noncompactness in the space BC.R C / which was introduced by Banas in [5]. Fix a nonempty bounded subset X of BC.R C / and a positive number K > 0.…”

“…Banas [5] proved that the above function is a measure of noncompactness in the space BC.R C /. Now, the existence of solutions for the integral equations (4.1) is studied under the following assumptions.…”

An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations

“…Banas [5] constructed a measure of noncompactness in the space BC(R + ). To present that measure, let us fix a nonempty bounded subset X of BC(R + ) and a positive number K > 0.…”