Fixed-point theorems using interpolative Boyd-Wong-type contractions and interpolative Matkowski-type contractions on partial $b$-metric spaces
Problemy analiza, Tome 14 (2025) no. 1, pp. 107-118.

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This article introduces interpolative contractions of both Boyd-Wong and Matkowski types in the framework of partial $b$-metric spaces. We derive fixed-point theorems for these two contractions and incorporate examples to emphasize the practical relevance of our findings.
Keywords: partial $b$-metric space, interpolative Boyd-Wong contraction, interpolative Matkowski contraction, fixed point.
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A. Gupta; R. Mansotra. Fixed-point theorems using interpolative Boyd-Wong-type contractions and interpolative Matkowski-type contractions on partial $b$-metric spaces. Problemy analiza, Tome 14 (2025) no. 1, pp. 107-118. http://geodesic.mathdoc.fr/item/PA_2025_14_1_a6/

[1] Aydi H., Karapinar E., Radenovic S., “On Interpolative Boyd-Wong type and Matkowski type contractions”, TWMS J. Pure Appl. Math., 11:2 (2020), 204–212 | MR | Zbl

[2] Aydi H., Chen C. M., Karap?nar E., “Interpolative ?iri?-Reich-Rus Type Contractions via the Branciari Distance”, Mathematics, 7:1 (2019), 84 | DOI

[3] Aydi H., Karapinar E., Roldan Lopez de Hierro A.F., “$\omega$-interpolative Ciric-Reich-Rus-type contractions”, Mathematics, 7:1 (2019), 5 | DOI

[4] Banach S., “Sur les opirations dans les ensembles abstraits et leur applications aux iquations intigrales”, Fundam. Math., 3:1 (1992), 133–181 | MR

[5] Boyd D. W., Wong J., “On Nonlinear Contractions”, Proc. Amer. Math. Soc., 20:2 (1969), 458–464 | DOI | MR | Zbl

[6] Czerwik S., “Contraction mappings in $b$-metric spaces”, Acta Math. Inform. Univ. Ostra., 1:1 (1993), 5–11 | MR | Zbl

[7] Chang Y., Guan H., “Generalized $ (\alpha_{s}, \xi, \hbar, \tau) $-Geraghty contractive mappings and common fixed point results in partial $ b $-metric spaces”, AIMS Math., 9:7 (2024), 19299–19331 | DOI | MR

[8] Debnath P., Mitrovic Z., Radenovic S. N., “Interpolative Hardy-Rogers and Reich-Rus-Ciric type contractions in $b$-metric spaces and rectangular $b$-metric spaces”, Mat. Vesnik, 72:4 (2020), 368–374 | MR | Zbl

[9] Kannan R., “Some results on fixed points”, Bull. Cal. Math. Soc., 60:10 (1968), 71–76 | MR | Zbl

[10] Karapinar E., Agarwal R., Aydi H., “Interpolative Reich-Rus-Ciric type contractions on partial metric spaces”, Mathematics, 6:11 (2018), 256 | DOI | Zbl

[11] Karap?nar E., “A survey on interpolative and hybrid contractions”, Mathematical Analysis in Interdisciplinary Research, Springer Optimization and Its Applications, 179, Springer, 2021, 431–475 | DOI | MR | Zbl

[12] Karapinar E., “Revisiting the Kannan type contractions via interpolation”, Adv. Theory Nonlinear Anal. Appl., 2:2 (2018), 85–87 | DOI | Zbl

[13] Karapinar E., Alqahtani O., Aydi H., “On Interpolative Hardy-Rogers Type Contractions”, Symmetry, 11:1 (2019), 8 | DOI | Zbl

[14] Michael B., Ralph K., Steve M., Homeira P., “Partial Metric Spaces”, Amer. Math. Monthly, 116:8 (2009), 708–718 | DOI | MR | Zbl

[15] Matkowski J., “Fixed point theorems for mappings with a contractive iterate at a point”, Proc. Amer. Math. Soc., 62:2 (1977), 344–348 | DOI | MR | Zbl

[16] Shahgari M. S., Ogbumba R.O., Yahaya S., “A new approach to Jaggi-Wardowski type fixed point theorems”, Probl. Anal. Issues Anal., 13(31):1 (2024), 50–70 | DOI | MR

[17] Shukla S., “Partial $b$-metric spaces and fixed point theorems”, Mediterr. J. Math., 11:2 (2014), 703–711 | DOI | MR | Zbl

[18] Puvar S. V., Vyas R. G., “Ciric-type results in Quasi-metric spaces and G-metric spaces using simulation function”, Probl. Anal. Issues Anal., 11(29):2 (2022), 72–90 | DOI | MR | Zbl

[19] Puvar S. V., Vyas R. G., “Rational Type ciric contraction in G-metric space”, Probl. Anal. Issues Anal., 12(30):3 (2023), 119–131 | DOI | MR | Zbl