Sentence examples for mappings in complete from inspiring English sources

Most recently, Samet et al. [12, 15] defined an α-ψ-contractive and α-admissible mapping and proved fixed point theorems for such mappings in complete metric spaces.

Most recently, Samet et al. [36] have defined α-ψ-contractive and α-admissible mapping and proved fixed point theorems for such mappings in complete metric spaces.

They also proved a fixed point theorem for α, ψ contractive mappings in complete metric spaces using the concept of α-admissible mapping.

They proved a fixed point theorem for such mappings in complete metric spaces.

Also, they proved some fixed point results for such mappings in complete metric spaces.

Moreover, some authors established fixed-point theorems for such mappings in complete fuzzy metric spaces.

Rhoades [28] extended Banach's principle by introducing weakly contractive mappings in complete metric spaces.

Next, we give some fixed point result for multiplicative -Banach-contraction mappings in complete multiplicative metric spaces.

Also, we analyze the existence and uniqueness of fixed points for such mappings in complete metric spaces.

As applications, we establish some common fixed point theorems for Lipschitz-type multi-valued mappings in complete metric spaces.

These classes of mappings are defined for multi-valued mappings in complete metric spaces endowed with directed graphs.