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

## TL;DR

This paper proves the existence of solutions for certain multivalued nonlinear Volterra integral equations in infinite-dimensional spaces using a measure of nonequicontinuity, introducing new fixed point theorems and compactness criteria.

## Contribution

It presents novel fixed point results for admissible condensing operators and establishes a weak compactness criterion in the space of locally integrable functions.

## Key findings

- Existence of solutions for multivalued Volterra integral inclusions in Fréchet spaces.
- New fixed point theorems for admissible condensing operators.
- A weak compactness criterion in Bochner integrable function spaces.

## Abstract

The existence of continuous not necessarily bounded solutions of nonlinear functional Volterra integral inclusions in infinite dimensional setting is shown with the aid of the measure of nonequicontinuity. New abstract topological fixed point results for admissible condensing operators are introduced. Weak compactness criterion in the space of locally integrable functions in the sense of Bochner is set forth. Some examples illustrating the usefulness of the presented approach are also included.