Sentence examples for mappings contains from inspiring English sources

(i)⇒ (ii): Suppose that every asymptotic TJ mapping of C into itself has a fixed point in C. Since the class of asymptotic TJ mappings contains the class of nonexpansive mappings, every nonexpansive mapping of C into itself has a fixed point in C. By Theorem 1.4, C is bounded.

Each relatively nonexpansive mapping is closed; The class of quasi-ϕ-asymptotically nonexpansive mappings contains properly the class of quasi-ϕ-nonexpansive mappings as a subclass, but the converse is not true; The class of quasi-ϕ-nonexpansive mappings contains properly the class of relatively nonexpansive mappings as a subclass, but the converse may be not true.

This implies that the class of φ-quasi-nonexpansive mappings contains strictly that of contraction mappings.

Thus the class of super hybrid mappings contains generalized hybrid mappings.

Clearly, the class of relatively asymptotically nonexpansive mappings contains the class of relatively nonexpansive mappings.

Theorem 3.2 generalizes Theorem 1.2 since the class of asymptotic TJ mappings contains the class of nonexpansive mappings.

Note that the class of λ-hybrid mappings contain the classes of nonexpansive mappings, nonspreading mappings, and hybrid mappings.

These two classes of nonlinear mappings contain some important classes of nonlinear mappings, like nonexpansive mappings and nonspreading mappings.

Recently, García-Falset et al. [7] introduced two generalizations of nonexpansive mappings which in turn include Suzuki generalized nonexpansive mappings contained in [24].

Algorithmically, in the implementation of the method, W is computed by forming the cross-product of the block-to-cloud mappings contained in V.

Recently, García-Falset et al. [6] introduced two generalizations of nonexpansive mappings which in turn include Suzuki generalized nonexpansive mappings contained in [7] and also utilized the same to prove some fixed point theorems.