Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness

Some generalizations of Darbo’s theorem and applications to fractional integral equations

“…All authors read and approved the final manuscript. 4 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland.…”

Some fixed point results via measure of noncompactness

“…Now, if there exists an N ∈ N such that σ(X N ) = 0, then X N is relatively compact. By (2) and (3), we also have that T (X N ) ⊂ X N . Thus, by Schauder fixed point theorem, we deduce that T has a fixed point.…”

“…Later, Aghajani et al [2] introduced the concept of a Meir-Keleer condensing operator and proved some fixed point results.…”

Application measure of noncompactness and operator type contraction for solvability of an infinite system of differential equations in lp-space

“…Now suppose that Fix(T) = {x ∈ Ω : Tx = x} and 0 = O( f ; G(µ(Fix(T)), ϕ(µ(Fix(T)))). If 0 0 then by (2) and T(Fix(T)) = Fix(T), we have…”