Geodesic
Common fixed point in $G$-metric spaces via generalized $\Gamma$-$C_F$-simulation function
Problemy analiza, Tome 13 (2024) no. 3, pp. 64-78.

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We present the generalized $\Gamma$-$C_F$-simulation function and establish the common fixed point result for weak $(\eta_F, g)$-contraction in complete $G$-metric space. The exploration extends to its ramifications on both quasi-metric spaces and metric spaces. The study explores the existence of a solution for a non-linear integral equation as an application of these results.
Keywords: $\Gamma$-$C_{F}$-simulation functions, $G$-metric spaces, quasi-metric spaces, weak contraction, common fixed point. 
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S. V. Puvar; R. G. Vyas. Common fixed point in $G$-metric spaces via generalized $\Gamma$-$C_F$-simulation function. Problemy analiza, Tome 13 (2024) no. 3, pp. 64-78. http://geodesic.mathdoc.fr/item/PA_2024_13_3_a4/

[1] Agarwal R. P., Kadelburg Z., Radenovic S., “On coupled fixed point results in asymmetric G-metric spaces”, Journal of Inequalities and Applications, 2013 (2013), 1–12 | DOI | MR | Zbl

[2] Agarwal R. P., Karapinar E., O'Regan D., Roldán-López-De Hierro A. F., Fixed point theory in metric type spaces, Springer, 2015 | MR | Zbl

[3] Ansari A. H., “Note on $\varphi$-$\psi$-contractive type mappings and related fixed point”, The 2nd Regional Conference on Math. Appl. (PNU, Sept. 2014), 377–380

[4] Banach S., “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales”, Fundam. Math., 3:1 (1922), 133–181 | DOI | MR

[5] Berinde V., Rus I. A., “Asymptotic regularity, fixed points and successive approximations”, Filomat, 34:3 (2020), 965–981 | DOI | MR | Zbl

[6] Chanda A., Dey L. K., Radenovic S., “Simulation functions: a survey of recent results”, Revista de la Real Academia de Ciencias Exactas, Fnsicas y Naturales. Serie Mathematics, 111:3 (2019), 2923–2957 | DOI | MR

[7] Jleli M., Samet B., “Remarks on G-metric spaces and fixed point theorems”, Fixed Point Theory Appl., 2012:1 (2012), 210, 7 pp. | DOI | MR | Zbl

[8] Karap?nar E., Joonaghany G. H., Khojasteh F., “Study of $\Gamma $-simulation functions, $Z_\Gamma$-contractions and revisiting the $L$-contractions”, Filomat, 35:1 (2021), 201–224 | DOI | MR | Zbl

[9] Khojasteh F., Shukla S., Radenovic̀ S., “A new approach to the study of fixed point theory for simulation functions”, Filomat, 29:6 (2015), 1189–1194 | DOI | MR | Zbl

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

[11] Puvar S. V., Vyas R. G., “Almost Suzuki type common fixed point result via extended $\Gamma$-$C_F$-simulation functions”, Adv. Math. Sci. Appl., 33:1 (2024), 217–229

[12] Radenovic S., Vetro F., Vujakovic J., “An alternative and easy approach to fixed point results via simulation functions”, Demonstratio Mathematica, 50:1 (2017), 223–230 | DOI | MR | Zbl

[13] Radenovic S., Chandok S., “Simulation type functions and coincidence points”, Filomat, 32:1 (2018), 141–147 | DOI | MR | Zbl

[14] Samet B., Vetro C., Vetro F., “Remarks on G-metric spaces”, Intern. J. Anal., 2013 (2013), 6 pp. | DOI | MR

[15] Zead M., Brailey S., “A new approach to generalized metric spaces”, J. Nonlinear Convex Anal., 7:2 (2006), 289–297 | MR | Zbl