Korean J. Math. Vol. 32 No. 1 (2024) pp.15-25
DOI: https://doi.org/10.11568/kjm.2024.32.1.15

Common fixed point theorems for three mappings in generalized modular metric spaces

Main Article Content

Sheela Arockiam
Maria Joseph John

Abstract

In this paper, we obtain common fixed point theorems for three mappings of contractive type in the setting of generalized modular metric spaces. Our results generalize many results available in the literature including common fixed point theorems.



Article Details

References

[1] A.A.N. Abdou, Fixed points of Kannan maps in modular metric spaces, AIMS Mathematics 5 (6) (2020), 6395–6403. https://doi.org/10.3934/math.2020411 Google Scholar

[2] A. Branciari, “A fixed point theorem of Banach- Caccippoli type on a class of generalized metric spaces”, Publ. Math. Debrecen, 57 (1-2) (2000) 31–37. Google Scholar

[3] A. Gholidahneh, S. Sedghi, O. Ege, Z. D. Mitrovic and M. de la Sen, The Meir-Keeler type contractions in extended modular b-metric spaces with an application, AIMS Mathematics, 6 (2) (2021) 1781–1799. https://doi.org/10.3934/math.2021107 Google Scholar

[4] Aleksa Malˇceski, Samoil Malˇceski, Katerina Anevska and Risto Malˇceski, New Extension of Kannan and Chatterjea Fixed Point Theorems on Complete Metric Spaces, British Journal of Mathematics and Computer Science, 17 (1) (2016) 1–10. https://doi.org/10.9734/BJMCS/2016/25864 Google Scholar

[5] Alexandru-Darius Filip and Adrian Petru ̧sel, Fixed Point Theorems on Spaces Endowed with Vector-Valued Metrics, Hindawi Publishing Corporation Fixed Point Theory and Applications, (2010). https://doi.org/10.1155/2010/281381 Google Scholar

[6] Al Pervo On the Cauchy problem for a system of ordinary differential equations, Pvi-blizhen met Reshen Diff Uvavn, 2 (1964) 115–134. Google Scholar

[7] A. Sheela and U. Karuppiah, A note on Nadler’s fixed point theorem in modular generalized metric space, JP Journal of Fixed Point Theory and Applications, 14 (3) (2019) 107–114. http://dx.doi.org/10.17654/FP014030107 Google Scholar

[8] C. Alaca, M.E. Ege and C. Park, Fixed point results for modular ultrametric spaces, Journal of Computational Analysis and Applications, 20 (7) (2016) 1259–1267. Google Scholar

[9] G.A. Okeke, D. Francis and M. de la Sen, Some fixed point theorems for mappings satisfying rational inequality in modular metric spaces with applications, Heliyon, 6 (8) (2020) e04785. https://doi.org/10.1016/j.heliyon.2020.e04785 Google Scholar

[10] H. Hosseinzadeh and V. Parvaneh, MeirKeeler type contractive mappings in modular and partial modular metric spaces, Asian-European Journal of Mathematics, 13 (1) (2020) 20500874. 5 https://doi.org/10.1142/S1793557120500874 Google Scholar

[11] M.E. Ege and C. Alaca, Fixed point results and an application to homotopy in modular metric spaces, Journal of Nonlinear Science and Applications, 8 (6) (2015), 900–908. http://dx.doi.org/10.22436/jnsa.008.06.01 Google Scholar

[12] M.E. Ege and C. Alaca, Some properties of modular S-metric spaces and its fixed point results, Journal of Computational Analysis and Applications, 20(1) (2016) 24–33. Google Scholar

[13] M.E. Ege and C. Alaca, Some Results for Modular b-Metric spaces and an Application to System of linear Equations, Azerbaijan Journal of Mathematics, 8 (1) (2018), 3–14. ISSN 2218-6816 Google Scholar

[14] M. Ramezani, H. Baghani, O. Ege and M. De la Sen, A new version of Schauder and Petryshyn type fixed point theorems in s-modular function spaces, Symmetry-Basel, 12 (1) (2020), 1–8. https://doi.org/10.3390/sym12010015 Google Scholar

[15] Muhammad Usman Ali, Tayyab Kamran, Hassan Houmani and Mihai Postolache, On the Solution of a System of Integral Equations via Matrix Version of Banach Contraction Principle, Communications in Mathematics and Applications, 8 (3) (2017) 207–215. https://www.rgnpublications.com/journals/index.php/cma/article/view/548 Google Scholar

[16] R. Kannan, Some Results on Fixed Points—II, MATHEMATICAL NOTES, The American Mathematical Monthly, 76(4) (1969) 405–408. https://doi.org/10.2307/2316437 Google Scholar

[17] S. K. Chatterjea, Fixed Point Theorems, C.R. ACad., Bulgare Sci, 25 (1972), 727–730. Google Scholar

[18] Xian Zhang, Common fixed point theorems for some new generalized contractive type mappings, Journal of Mathematical Analysis and Applications, 333 (2) (2007), 780–786. https://doi.org/10.1016/j.jmaa.2006.11.028 Google Scholar