Geodesic
Some new fixed point results in $\mathrm{b}$-metric space with rational generalized contractive condition
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 506-518

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In this paper, we improve and generalize several results in fixed point theory to the $\mathrm{b}$-metric space. Where we confirm the existence of the fixed point for self mapping $T$ satisfying some rational contractive conditions. Over-more, we establish the uniqueness of the fixed point in some cases and give dynamic information linking the fixed points between them in the other cases. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses.
Keywords: metric space, $\mathrm{b}$-metric space, Picard sequence, Fixed point, Rational contraction mapping. 
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     author = {Besma Laouadi and Taki Eddine Oussaeif and Leila Benaoua and Liliana Guran and Stojan Radenovi\'c},
     title = {Some new fixed point results in $\mathrm{b}$-metric space with rational generalized contractive condition},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a8/}
}
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Besma Laouadi; Taki Eddine Oussaeif; Leila Benaoua; Liliana Guran; Stojan Radenović. Some new fixed point results in $\mathrm{b}$-metric space with rational generalized contractive condition. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 506-518. http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a8/