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Monotonicity properties of the superposition operator and their applications |
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| Authors: | Jzef Bana Kishin Sadarangani |
| Institution: | aDepartment of Mathematics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland;bDepartment of Mathematics, University of Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain |
| Abstract: | We establish some properties of the superposition operator which are associated with monotonicity. Those properties are expressed in terms of the notion of degree of decrease or degree of increase. An application of the obtained results to the study of solvability of a quadratic Volterra integral equation is also derived. |
| Keywords: | Superposition operator Degree of decrease Measure of noncompactness Quadratic integral equation Fixed point theorem |
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