Sentence examples for mappings one can from inspiring English sources
For the example of a one-parameter continuous semigroup of nonexpansive mappings, one can see [18].
For other net-terminology properties about these two mappings, one can refer to [12].
In a similar way as for nonexpansive mappings, one can develop a theory for the classes of mappings introduced in this section.
For instance, in [40] Fukumizu et al. showed by optimizing kernel mappings one can find the most predictive subspace in regression.
Yamada's method is then extended to solve more complex problems involving finite or infinite nonexpansive mappings (one can refer to, e.g., [18, 19] and the references therein).
Since the class of relatively nonexpansive mappings is properly contained in the class of total quasi-φ-asymptotically nonexpansive mappings, for a finitely many mappings case, one can derive the desired result from Theorem 2.1.
This summary does not distinguish between two mappings if one can be continuously deformed to the other; thus, only equivalence classes of mappings are summarized.
If one replaces the respective one parameter semigroups of generalized Lipschitzian mappings in Theorems 3.1 and 3.2 with respective semigroups of iterates of generalized Lipschitzian mappings, then one can immediately derive the following two corollaries.
In brief, for suitable choices of the mappings and, one can obtain a number of known and new variational inequalities and variational-like inequalities as special cases of (2.1).
Evidently, for appropriate and suitable choice of the fuzzy mappings, mappings, the bifunction, and the space, one can obtain a number of the known classes of variational inequalities and variational-like inequalities as special cases from problem (2.5) (see [1, 4, 5, 7 19]).
It can be observed that in the case of two mappings A, S:X → X, one can consider the following classes of mappings for the existence and uniqueness of common fixed points: d ( Ax, Ay ) ≤ F ( m ( x, y ) ), Open image in new window (1.1).
