Sentence examples for also for the self-map from inspiring English sources

Also, for the self-map.

Define also the composed self-map as from the self-map whose restrictions to,, are defined via the restriction ; by for each ;.

for some which is a contradiction, and the self-map (and then the self-map ) of is nonexpansive and property (i) holds.

If the self-map of is nonexpanding, then, for all, [8].

The potential discontinuity points of such a self-map in a discrete subset are the so-called switching points at which a new primary self-map in a class is activated to construct the self-map of interest, each of those self-maps depends also on some given switching rule.

It is not difficult to see that the property also holds if the primary self-maps are large contractions or there are mixed large and strict contractions used by the switching rule to build the self-map Each particular fixed point may depend on the switching rule and is a fixed point space for the class of self-maps built in such a way.

Then, the self-map the Lipschitzian self-map from to has a fixed point in.

is also the only fixed point of the self-mapping on in the complete metric space defined by ; which is -contractive for any real provided that.

Now, the self-mapping is defined as for each such that for some ; such that.

It was proved in [23] (see also [24]) that a self-map of a complete metric space has a unique fixed point if for some nonnegative scalars, with and for all, the inequality.

Define the self-mapping on as ;.