scholarly journals Proximinality and co-proximinality in metric linear spaces

2015 ◽  
Vol 69 (1) ◽  
pp. 83
Author(s):  
T. W. Narang ◽  
Sahil Gupta
Keyword(s):  
Best Approximation ◽  
Existence And Uniqueness ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Best Coapproximation ◽  
Uniqueness Of Best Approximation

As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces.

scholarly journals Proximinality and co-proximinality in metric linear spaces

2015 ◽  
Vol 69 (1) ◽  
Author(s):  
T.D. Narang ◽  
Sahil Gupta
Keyword(s):  
Best Approximation ◽  
Existence And Uniqueness ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Best Coapproximation ◽  
Uniqueness Of Best Approximation

AbstractAs a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces

scholarly journals Extensions of closed convex processes

2015 ◽  
Vol 31 (1) ◽  
pp. 31-37
Author(s):  
A. R. BAIAS ◽  
◽  
T. TRIF ◽  
Keyword(s):  
Best Approximation ◽  
Convex Cones ◽  
Linear Spaces ◽  
Convex Processes ◽  
Normed Linear Spaces

In this paper we provide some norm preserving extension results for real valued closed convex processes. As a consequence, we characterize afterwards, the elements of best approximation in normed linear spaces by elements of closed convex cones using closed convex processes.

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