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Article
Metrically round and sleek metric spaces
A round metric space is the one in which the closure of each open ball is the corresponding closed ball. By a sleek metric space, we mean a metric space in which the interior of each closed ball is the corresp...
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Article
Remarks on balls in metric spaces
In this article we discuss metric spaces in which closure of open balls are the corresponding closed balls, and interior of closed balls are the corresponding open balls. Moreover, we try to explore relationsh...
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Article
Convex linear metric spaces are normable
A linear metric space (X, d) is called a convex linear metric space if for all x, y in X, it also satisfies \(d(\lambda x+(1-\lambda )y,0)\le \lambda d(x,0)+(1-\lambda )d(y,0)\) d ( λ x + ( 1 - λ ) y , 0 ) ≤ λ
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Chapter and Conference Paper
Best Simultaneous Approximation in Quotient Spaces
We discuss the problem of best simultaneous approximation in quotient spaces when the underlying spaces are metric linear spaces. We characterize simultaneous proximinality, simultaneous Chebyshevity, simultan...
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Article
Common fixed points and invariant approximation for Gregus type contraction map**s
Some new common fixed point theorems for Gregus type contraction map**s have been obtained in convex metric spaces. As applications, invariant approximation results for these types of map**s are obtained. ...
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Article
Common fixed points and invariant approximation of R-subweakly commuting maps in convex metric spaces
Sufficient conditions for the existence of a common fixed point of R-subweakly commuting map**s are established within the framework of a convex metric space. As applications, we obtain various results on the b...
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Article
Generalizations of Ky Fan’s theorem on best approximations
In 1969, Ky Fan[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x ∈ M such that ‖f(x) − x‖ = dist(f(x),M). Since then, there have appear...
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Article
Some results on best approximation in spaces with convex structure
Some generalizations of the result proved by S. P. Singh [J. Approx. Theory 25(1979), 89–90] are presented in convex metric spaces. The results proved contain several known results on the subject.
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Article
On the uniqueness of best approximation in non-archimedian spaces
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Article
On singletonness of uniquely remotal sets
