Existence and uniqueness of fixed points of an integral operator of Hammerstein type

F. H. Khaidarov<sup>ab

a</sup> Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan
^b AKFA University, Tashkent, Uzbekistan

Abstract: We study the existence and uniqueness of positive fixed points of an integral operator of the Hammerstein type in the space of continuous functions. Under certain conditions on the integral operator, we establish a sufficient condition for the the integral operator to have exactly one positive fixed point.

Keywords: Hammerstein integral operator, positive fixed point, existence, uniqueness, cone, normal cone.

Received: 27.02.2021
Revised: 27.02.2021

DOI: 10.4213/tmf10083

 English version: Theoretical and Mathematical Physics, 2021, 208:3, 1228–1238

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