Geodesic
A new generalization of metric spaces satisfying the $T_2$-separation axiom and some related fixed point results
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 58-70.

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In this paper, without using neither the compactness nor the uniform convexity, some fixed point theorems are proved by using a binary relation in the setting of a new class of spaces called $T$-partial metric spaces. This class of spaces can be considered the first generalization of metric spaces such that the generated topology is a Hausdorff topology. Our theorems generalize and improve very recent fixed point results in the literature. Finally, we show the existence of a solution for a class of differential equations under new weak conditions.
Keywords: fixed point, $T$-partial metric space, uniform convexity, $T_2$ separation axiom, integral equation. 
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     title = {A new generalization of metric spaces satisfying the $T_2$-separation axiom and some related fixed point results},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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}
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Y. Touail. A new generalization of metric spaces satisfying the $T_2$-separation axiom and some related fixed point results. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 58-70. http://geodesic.mathdoc.fr/item/IVM_2023_5_a6/

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