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Best proximity point theorems: an exploration of a common solution to approximation and optimization problems. (English) Zbl 1245.90120
Summary: Given a non-self mapping $T:A\to B$ in the setting of a metric space, this work concentrates on the resolution of the non-linear programming problem of globally minimizing the real valued function $x\to d(x,Tx)$, thereby yielding an optimal approximate solution to the equation $Tx=x$. An iterative algorithm is also presented to compute a solution of such problems. As a sequel, it is possible to compute an optimal approximate solution to some non-linear equations.

90C30Nonlinear programming
65K05Mathematical programming (numerical methods)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
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