Abstract
We discuss the existence and uniqueness of solutions to the minimization problem \({{\rm min}_{x \epsilon A} d(x, Tx)}\), where A, B are nonempty subsets of a partially ordered set X endowed with a metric d, and \({T : A \to B}\) is a non-self-mapping satisfying a proximal contraction of Meir–Keeler type (MK-proximal contraction). An iterative algorithm is also provided to approximate the optimal solution. As particular cases of our obtained results, various fixed point theorems on a metric space endowed with a partial order are deduced.
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