The class of generalized asymptotically quasi-ϕ-nonexpansive mappings is a generalization of the class of generalized asymptotically quasi-nonexpansive mappings in the framework of Banach spaces.
Remark 3.2 Since the class of generalized asymptotically quasi-ϕ-nonexpansive mappings is a generalization of the class of asymptotically quasi-ϕ-nonexpansive mappings, Theorem 3.1 includes Kim's [36] results as a special case.
Indeed, the above mentioned function classes are generalizations of the general meromorphic starlike, meromorphic convex, meromorphic close-to-convex and meromorphic quasi-convex functions in analytic function theory (see, for details, [3 12]).
For all the classes, the generalization rate of FFS is higher than this of PFS, showing the pertinent rule of the auditory threshold.
Finally, the fact that familiarity did not modify within-class responses demonstrates a capacity of generalization, which is one of the cue properties of categorization.
This way the number of known classes and generalization error are both bounded in the same range (between 0 and 1) and we can conveniently represent them on the same chart.
A second generalization to classes of algebras, rather than merely to individual algebras, was also crucial to the mathematical development of the subject matter.
Corollaries 3.7 and 3.13, are interesting for defining the concepts of other classes of nonlinear mappings which are generalizations of several well-known mappings due to Chatterjea [10], Ćirić [11], Geraghty [12], Meir and Keeler [13], Mizoguchi and Takahashi [14], Suzuki [15], etc.
While the LC/MS data provide extensive information about the labeling of specific metabolites, it is difficult to make generalizations about classes of compounds given the thousands of rows in the XCMS table and the difficulty in identifying each.
