APPLICATION OF MEASURES OF WEAK NONCOMPACTNESS TO A NONLOCAL DARBOUX PROBLEM

Application of measures of noncompactness to infinite system of linear equations in sequence spaces

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.  

Inequivalent measures of noncompactness

Two homogeneous measures of noncompactness β and γ on an infinite dimensional Banach space X are called “equivalent” if there exist positive constants b and c such that bβ(S) ≤ γ (S) ≤ cβ(S) for all bounded sets S ⊂ X . If such constants do not exist, the measures of noncompactness are “inequivalent.”Weask a foundational questionwhich apparently has not previously been considered: For what infi...

Construction of measures of noncompactness of $C^k(Omega)$ and $C^k_0$ and their application to functional integral-differential equations

‎In this paper‎, ‎first‎, ‎we investigate the construction of compact sets of $ C^k$ and $ C_0^k$‎ ‎by proving ``$C^k‎, ‎C_0^k-version$‎" ‎of Arzel`{a}-Ascoli theorem‎, ‎and then introduce new measures of noncompactness on these spaces‎. ‎Finally‎, ‎as an application‎, ‎we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixe...

application of measures of noncompactness to infinite system of linear equations in sequence spaces

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.

Existence of Solution to a Second-Order Boundary Value Problem via Noncompactness Measures