In 2001, Rhoades [[2], Theorem 2] obtained a generalization of Banach's contraction mapping principle [Note the weakly con-traction contains contraction as the special case (ϕ(t) = 1-k tt)].
Note that the class of quasi-contractive mappings already contains contractions, Kannan, Chatterji and Zamfirescu operators (for definitions, see [18]).
The problem is to label automatically time episodes containing contractions so that only a fraction of the video needs inspection.
Also, Rhoades [3] proved the following very interesting fixed point theorem which contains contractions as special case.
In 2001, Rhoades [2] proved the following very interesting fixed point theorem which is one of generalizations of Theorem 1.1 because the weakly contractions contains contractions as the special cases.
Thereafter, in 2001, Rhoades [5] proved the fixed point theorem which is one of the generalizations of Banach's contraction mapping principle because the weakly contractions contain contractions as a special case, and he also showed that some results of [4] are true for any Banach space.
When obtained, endomyocardial biopsies contained nonspecific contraction band necrosis [9].
The ventral abdomen contracts an average of 52.8 times per minute, but these contractions are aggregated within distinct contraction periods (consecutive contractions without rest) that last an average of 2.83 sec and contain 5.37 contractions each, indicating that when the abdomen contracts it does so at a rate of 1.98 Hz (Table 1).
Nadler used the concept of Hausdorff metric to establish the multivalued contraction principle containing the Banach contraction principle as a special case.
He used the concept of the Hausdorff metric to establish the multivalued contraction principle containing the Banach contraction principle as a special case.
He used the concept of a Hausdorff metric ℋ to establish the multivalued contraction principle containing the Banach contraction principle as a special case as follows.
