ON CUBIC INTEGRAL EQUATIONS OF URYSOHN-STIELTJES TYPE

Authors

  • M. A. Darwish Department of Mathematics, Faculty of Sciences, Damanhour University, Egypt Author
  • D. O'Regan School of Mathematics, National University of Ireland, Galway, Ireland Author

Keywords:

Cubic integral equation, Urysohn, Stieltjes, nondecreasing solutions, measure of noncompactness, Darbo's fixed point theorem

Subjects:

45G10, 47H30

Abstract

In this paper, we establish an existence theorem for a cubic Urysohn-Stieltjes integral equationin the Banach space $C([0,1])$. The equation under consideration is a general form ofnumerous integral equations encountered in the theory of radioactivetransfer, in the kinetic theory of gases and in the theory of neutron transport. Our main tools are themeasure of noncompactness (related to monotonicity) and a fixed point theorem dueto Darbo.

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Published

2021-07-15

Issue

Vol. 73 No. 3 (2021): Vol. 73, Issue 3

Section

Articles

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