Some new extensions of Darbo's fixed point theorem with application

Abstract

We present some new extensions of Darbo's fixed-point theorem with a
different aspect than those available in the literature by introducing the
concept of $(k,L)$-set contraction. The concept of $(k,L)$-set contraction
is interesting since there is no restriction for the constant $L$. We also
present the nonlinear Leray-Schauder type alternative for one of our
results. Finally, to demonstrate the applicability, we utilize theoretical
results to provide the existence of solution of an integral equation.