Abstract

Some topological properties of generalized $2$-normed (G2N) spaces have been studied in this article. The notion of $g$-convergence for sequences is introduced in general, and it is compared with the usual notion of convergence. It is shown that $g$-convergence is a more general idea, and under certain conditions $g$-convergence and convergence actually coincide. Using these concepts, a few fixed point theorems are developed.

Keywords: Generalized $2$-normed spaces; $g-3ps$ spaces; $G$-metric space; $S$-metric spaces; $g$-convergence.

MSC: 46B20, 47A30, 46S99, 55M20, 54H25, 47H10

DOI: 10.57016/MV-OQYT5360

Pages:  1--16