Abstract
In this paper, we study the existence of positive solutions for classes of nonlinear operator equations in Banach spaces ordered by cones. We establish new coincidence point theorems via a generalized monotone iterative method. As applications, we discuss the existence of positive solutions for systems of nonlinear matrix equations and a system of integral equations of Volterra type.
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The authors thank Professor Imed Kédim and the anonymous reviewer for their helpful comments.
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Communicated by Ti-Jun Xiao.
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Berzig, M., Bouali, M. Coincidence point theorems in ordered Banach spaces and applications. Banach J. Math. Anal. 14, 539–558 (2020). https://doi.org/10.1007/s43037-019-00007-3
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DOI: https://doi.org/10.1007/s43037-019-00007-3