Sentence examples for mappings defined from from inspiring English sources
Let {T1,...,T N } be a finite family of mappings defined from D into D. A mapping T : D → D is called a full word if T can be written as a finite product of the mappings {T1,..., T N }, where each T i will occur at least once.
Nadler [21] extended the Banach contraction principle for the set-valued mappings, that is, for the mappings defined from the space X into the set (operatorname{CB}(X)).
Let be a family of mappings defined from D into D. The fixed point set of is the set Fix ( T ) = ∩ T ∈ T Fix ( T ).
It must be stressed that Corollary 11 is related to Proposition 2 and Theorem 1 in [11], where fixed point results for expanding mappings defined from partially ordered complete metric spaces into itself have been proved.
Let {T1,..., T N } be a finite family of mappings defined from D into D, where D is a nonempty and closed subset of X. Assume that {T1,..., T N } are projective w.r.t. a common fixed point c ∈ D. Also assume that {Fix(T1),..., Fix(T N )} is innately boundedly regular.
Remark 5 Observe that the proof of Theorem 4 follows applying similar arguments to those given in the proof of Kleen's theorem or Tarski-Kantorovitch's theorem for mappings defined from ω-chain-complete ordered sets into itself (see [42, 43] for more details).
Therefore, some of the fixed theorems regarding contraction mappings defined via auxiliary functions from the set Ψ can be in fact deduced from the existing ones in the literature.
Similar approaches to those in the present paper can be done for mappings defined on product spaces but adapted from the ones in the usual case; see the recent related fixed point results [38 42], and [43].
Let T be a family of nonexpansive mappings defined on H. Assume any two mappings from T form a symmetric Banach operator pair.
Let T be an invertible semigroup of isometric mappings defined on H such that any two mappings from T form a symmetric Banach operator pair.
Let T be a family of order preserving mappings defined on X. Assume any two mappings from T form a symmetric Banach operator pair.
