Sentence examples for mappings by considering from inspiring English sources

Hyers' theorem was generalized by Rassias [3] for linear mappings by considering an unbounded Cauchy difference.

M. Rassias [4] for linear mappings by considering an unbounded Cauchy difference.

Also, Rassias [4] extended the same results to linear mappings by considering an unbounded cauchy difference.

Hyers' theorem was generalized by Themistocles M Rassias [13] for linear mappings by considering an unbounded Cauchy difference.

Hyers' theorem was generalized by Th.M. Rassias [3] for linear mappings by considering an unbounded Cauchy difference.

The Hyers' theorem was generalized by Aoki [2] and Bourgin [8] for additive mappings by considering an unbounded Cauchy difference.

Let us extend the above concept in a natural way to 2-cyclic Kannan self-mappings by considering the definition of 2-cyclic -contractions (1.1) as follows.

Dedekind also tends to do both, often in conjunction, by considering mappings on the systems studied, especially structure-preserving mappings (homomorphisms etc)., and what is invariant under them.

The Functional Ontology Enrichment tool, which was used for analysing 56 up-regulated genes by considering their mappings onto terms of a given MetaCore ontology, showed a number of significant (p<0.01) inflammatory pathways such as ChREBP regulation pathway and IFNα/β signalling pathway (Additional file 1: Table S1).

Best proximity point theorems establish a generalization of fixed points by considering self-mappings.

These results have been obtained by considering self-mappings that satisfy an explicit contractive-type condition.