Abstract
In this paper, we investigate the mixed monotone operators of a new type in a Cartesian product of a Banach space with an order determined by a normal cone. We establish sufficient conditions for such operators to have a unique fixed point and provide monotone iterative techniques which give sequences convergent to the fixed point. We also apply the obtained results to prove the existence and uniqueness of a solution of a nonlinear integral equation.
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Wardowski, D. Mixed monotone operators and their application to integral equations. J. Fixed Point Theory Appl. 19, 1103–1117 (2017). https://doi.org/10.1007/s11784-016-0335-7
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DOI: https://doi.org/10.1007/s11784-016-0335-7