983 research outputs found
A fixed point theoremfor nonexpansive compact self-mapping
A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject
Some Fixed Point Theorems for Kannan Mappings
2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.Some results on the existence and uniqueness of fixed points for Kannan mappings on admissible subsets of bounded metric spaces and on bounded closed convex subsets of complete convex metric spaces having uniform normal structure are proved in this paper. These results extend and generalize some results of Ismat Beg and Akbar Azam [Ind. J. Pure Appl. Math. 18 (1987), 594-596], A. A. Gillespie and B. B. Williams [J. Math. Anal. Appl. 74 (1980), 382-387] and of Yoichi Kijima and Wataru Takahashi [Kodai Math Sem. Rep. 21 (1969), 326-330]
Metrically Round and Sleek Metric Spaces
A round metric space is the one in which closure of each open ball is the
corresponding closed ball. By a sleek metric space, we mean a metric space in
which interior of each closed ball is the corresponding open ball. In this,
article we establish some results on round metric spaces and sleek metric
spaces.Comment: 13 pages, 10 Figure
On strong proximinality in normed linear spaces
The paper deals with strong proximinality in normed linear spaces. It is proved that in a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed
Round and sleek subspaces of linear metric spaces and metric spaces
In the recent work [Metrically round and sleek metric spaces, \emph{The
Journal of Analysis} (2022), pp 1--17], the authors proved some results on
metrically round and sleek linear metric spaces and metric spaces. In
continuation, the present article discusses more results on such spaces along
with identification of round and sleek subsets of linear metric spaces and
metric spaces in the subspace topology.Comment: 14 pages, 1figur
Properties and occurrence rates of exoplanet candidates as a function of host star metallicity from the DR25 catalog
Correlations between the occurrence rate of exoplanets and their host star
properties provide important clues about the planet formation processes. We
studied the dependence of the observed properties of exoplanets (radius, mass,
and orbital period) as a function of their host star metallicity. We analyzed
the planetary radii and orbital periods of over 2800 candidates from
the latest data release DR25 (Q1-Q17) with revised planetary radii
based on ~DR2 as a function of host star metallicity (from the Q1-Q17
(DR25) stellar and planet catalog). With a much larger sample and improved
radius measurements, we are able to reconfirm previous results in the
literature. We show that the average metallicity of the host star increases as
the radius of the planet increases. We demonstrate this by first calculating
the average host star metallicity for different radius bins and then
supplementing these results by calculating the occurrence rate as a function of
planetary radius and host star metallicity. We find a similar trend between
host star metallicity and planet mass: the average host star metallicity
increases with increasing planet mass. This trend, however, reverses for masses
: host star metallicity drops with increasing planetary
mass. We further examined the correlation between the host star metallicity and
the orbital period of the planet. We find that for planets with orbital periods
less than 10 days, the average metallicity of the host star is higher than that
for planets with periods greater than 10 days.Comment: 14 pages, 13 Figures, Accepted for publication in The Astronomical
Journa
Proximinality and co-proximinality in metric linear spaces
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
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