On Best Proximity Point Theorems without Ordering
Copyright policy )On Best Proximity Point Theorems without Ordering
Recently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. He assumed that ifAandBare nonvoid subsets of a partially ordered set that is equipped with a metric andSis a non-self-mapping fromAtoB, then the mappingShas an optimal approximate solution, called a best proximity point of the mappingS, to the operator equationSx=x, whenSis a continuous, proximally monotone, ordered proximal contraction. In this note, we are going to obtain his results by omitting ordering, proximal monotonicity, and ordered proximal contraction onS.
- Naresuan University Thailand
- Razi University Iran (Islamic Republic of)
Artificial intelligence, Best Proximity Points, Fixed-point and coincidence theorems (topological aspects), Fixed Point Theorems, Nonconvex programming, global optimization, Computer science, Partial Ordering, Algorithm, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Geometry and structure of normed linear spaces, Fixed-point theorems, Fixed Point Theorems in Metric Spaces, Nonlinear programming, Physical Sciences, QA1-939, FOS: Mathematics, Geometry and Topology, Mathematics
Artificial intelligence, Best Proximity Points, Fixed-point and coincidence theorems (topological aspects), Fixed Point Theorems, Nonconvex programming, global optimization, Computer science, Partial Ordering, Algorithm, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Geometry and structure of normed linear spaces, Fixed-point theorems, Fixed Point Theorems in Metric Spaces, Nonlinear programming, Physical Sciences, QA1-939, FOS: Mathematics, Geometry and Topology, Mathematics
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