On some generalizations of the Mönch, Sadovskiĭ and Darbo fixed point theorems

Existence of solutions for a class of multivalued functional integral equations of Volterra type via the measure of nonequicontinuity on the Fréchet space ${\bf C(Ω,E)}$

“…Since F is admissible, T is compact as well. As we have seen in the proof of [21,Th.3. ], F : T ⊸ T is also an admissible multimap.…”

“…Proof. Keeping the notation and notions contained in the proof of [21,Th.3. ], consider a family {T α } α∈A of all fundamental subsets of previously defined multimap F : X ⊸ X containing x 0 .…”

Condensing Mappings and Best Proximity Point Results

“…Sadovskii [3], in 1967, defined condensing mappings and extended Darbo's theorem. Since then a lot of work has been done using this concept, and several interesting results have appeared, see, for instance, [4][5][6][7][8][9].…”

A Nonlinear F-Contraction Form of Sadovskii's Fixed Point Theorem and Its Application to a Functional Integral Equation of Volterra Type

“…then T has a fixed point. Some generalizations of these fixed point theorems can be found for example in [1,7,11] and the references therein.…”

“…Also, Theorem 1.1 can be easily generalized in the spirit of [11,Theorem 5]. Indeed, let Φ denote the set of all functions f : R + 2 → R satisfying…”