Solvability of nonlinear integral equations and surjectivity of nonlinear Markov operators

Farrukh Mukhamedov, Otabek Khakimov, Ahmad Fadillah Embong

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In the present paper, we consider integral equations, which are associated with nonlinear Markov operators acting on an infinite-dimensional space. The solvability of these equations is examined by investigating nonlinear Markov operators. Notions of orthogonal preserving and surjective nonlinear Markov operators defined on infinite dimension are introduced, and their relations are studied, which will be used to prove the main results. We show that orthogonal preserving nonlinear Markov operators are not necessarily satisfied surjective property (unlike finite case). Thus, sufficient conditions for the operators to be surjective are described. Using these notions and results, we prove the solvability of Hammerstein equations in terms of surjective nonlinear Markov operators.

Original languageEnglish
Pages (from-to)9102-9118
Number of pages17
JournalMathematical Methods in the Applied Sciences
Volume43
Issue number15
DOIs
Publication statusPublished - Oct 1 2020

Keywords

  • nonlinear integral equation
  • orthogonal preserving
  • polynomial stochastic operator
  • surjective

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering

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