Compactness result and its applications in integral equations
-
Mateusz Krukowski
and
Bogdan Przeradzki
Abstract
A version of the Arzelà–Ascoli theorem for X being a σ-locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn operators. Two fixed point theorems, for Hammerstein and Urysohn operators, are derived on the basis of Schauder fixed point theorem.
Acknowledgements
We would like to express our utmost gratitude to both referees for all comments and suggestions. The paper has benefited tremendously from all their remarks. With pleasure, we acknowledge the contribution of the referees.
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Articles in the same Issue
- Frontmatter
- On the cubic and cubic-quintic optical vortices equations
- Symmetry reductions and exact solutions to the Sharma–Tasso–Olever equation
- Simultaneously proximinal subspaces
- Iteration regularized semigroups of set-valued functions
- A recursive-operational approach with applications to linear differential systems
- On symmetrically porouscontinuous functions
- Compactness result and its applications in integral equations
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On statistically
- Ritz-least squares method for finding a control parameter in a one-dimensional parabolic inverse problem
