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Some extensions of banach contraction principle in G-metric spaces

Gaba Y. U.

Fasciculi Mathematici

2018

Nr 61

55--70

We present different extensions of the Banach contraction principle in the G-metric space setting. More precisely, we consider mappings for which the contractive condition is satisfied by a power of the mapping and for which the power depends on the specified point in the space. We first state the result in the continuous case and later, show that the continuity is indeed not necessary. Imitating some techniques obtained in the metric case, we prove that under certain conditions, it is enough for the contractive condition to be verified on a proper subset of the space under consideration. These results generalize well known comparable results.

Some advances in the theory of quasi-pseudometric type spaces

Gaba Y. U.

Fasciculi Mathematici

2016

Nr 56

61--76

In this paper, we extend most of the results proved in [4]. In particular, we give some topological properties of the quasi-pseudometric type spaces. Moreover, some fixed point and common fixed point theorems are obtained in the setting of quasi-pseudometric spaces, introduced some months ago by Kazeem et al in [4].