Sentence examples for mapping were proved from inspiring English sources

Best proximity point theorems for relatively u-continuous mapping were proved in [9] and [10].

Under suitable conditions, some strong converge theorems to a fixed point of the nonexpansive mapping are proved.

A particular case of Rassias' theorem regarding the Hyers-Ulam stability of the additive mapping was proved by Aoki (see [4]).

A strong convergence theorem of the proposed algorithm to a fixed point of a total quasi-asymptotically pseudo-contractive mapping is proved.

Under suitable conditions, some strong convergence theorems for the sequence generated by the algorithms to a fixed point of the nonexpansive mapping are proved.

The following more general common fixed point theorem for 1-subcommutative maps was proved in [12].

The counterpart to Theorem 3.1 for weakly contractive maps was proved by Frigon [8].

The specifications of the introduced special logistic maps are proved to be completely controlled through eight design problems with their Lyapunov exponent.

The existence of the conjugating map for the class of critical real analytic circle maps was proved by Yoccoz [8] and extended by Świątek [6, 7].

GDOES, in combination with X-SEM elemental maps, was proved to be a fast and accurate technique to monitor composition in-depth changes during oxidation, providing unique information regarding the oxide structure formation.

A best proximity pair for a set-valued map with respect to a set-valued map is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces.