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Comment: only one source does not establish notability; suggest adding another source or two, and cite all the examples and statements as they are unsourced.
ToadetteEdit! 07:59, 27 April 2024 (UTC)
is about a property called "common limit in the range" in fuzzy metric spaces
In mathematics, the notion of “common limit in the range” property denoted by CLRg property[1] is a theorem that unifies, generalizes, and extends the
contractive mappings in
fuzzy metric spaces, where the range of the
mappings does not necessarily need to be a
closedsubspace of a non-empty
set.
Suppose is a non-empty set, and is a distance metric; thus, is a metric space. Now suppose we have self
mappings These
mappings are said to fulfil CLRg property if
for some
Next, we give some examples that satisfy the CLRg property.
Examples
Example 1.
Suppose is a usual metric space, with Now, if the
mappings are defined respectively as follows:
for all Now, if the following sequence is considered. We can see that
thus, the
mappings and fulfilled the CLRg property.
Another example that shades more light to this CLRg property is given below
Example 2
Let is a usual metric space, with Now, if the
mappings are defined respectively as follows:
for all Now, if the following sequence is considered. We can easily see that
hence, the
mappings and fulfilled the CLRg property.
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