TY - JOUR
T1 - Solvability of nonlinear integral equations and surjectivity of nonlinear Markov operators
AU - Mukhamedov, Farrukh
AU - Khakimov, Otabek
AU - Embong, Ahmad Fadillah
N1 - Funding Information:
The author from UAEU would like to acknowledge financial support through “Start‐Up” Grant 31S259. Moreover, the author from UTM would like to acknowledge the Ministry of Higher Education (MOHE) and Research Management Centre‐UTM, Universiti Teknologi Malaysia (UTM), for the financial support through the research grant (Vote 17J93). Special thanks to anonymous reviewers for their contrustive comments, which improve the presentation of this paper.
Funding Information:
The author from UAEU would like to acknowledge financial support through ?Start-Up? Grant 31S259. Moreover, the author from UTM would like to acknowledge the Ministry of Higher Education (MOHE) and Research Management Centre-UTM, Universiti Teknologi Malaysia (UTM), for the financial support through the research grant (Vote 17J93). Special thanks to anonymous reviewers for their contrustive comments, which improve the presentation of this paper.
Publisher Copyright:
© 2020 John Wiley & Sons, Ltd.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - 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.
AB - 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.
KW - nonlinear integral equation
KW - orthogonal preserving
KW - polynomial stochastic operator
KW - surjective
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U2 - 10.1002/mma.6604
DO - 10.1002/mma.6604
M3 - Article
AN - SCOPUS:85086147884
SN - 0170-4214
VL - 43
SP - 9102
EP - 9118
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 15
ER -