Korean J. Math. Vol. 31 No. 2 (2023) pp.123-131
DOI: https://doi.org/10.11568/kjm.2023.31.2.123

Best proximity points for contractive mappings in generalized modular metric spaces

Main Article Content

V. Anbukkarasi
M. Marudai
R. Theivaraman


In this paper, we prove existence of best proximity points for 2-convex contraction, 2-sided contraction, and M-weakly cyclic 2-convex contraction mappings in the setting of complete strongly regular generalized modular metric spaces that generalize many results in the literature.

Article Details


[1] A.A.N. Abdou, Fixed points of Kannan maps in modular metric spaces, AIMS Mathematics 5 (6) (2020), 6395–6403. Google Scholar

[2] 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

[3] M.U. Ali, T. Kamran, H. Houmani and M. 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. Google Scholar

[4] V. S. Bright and M. Marudai, Fixed point theorem for weakly B-contractive mapping in ordered metric spaces, Gen. Math. notes 35 (2) (2016), 1–14. Google Scholar

[5] 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. Google Scholar

[6] 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

[7] 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. Google Scholar

[8] 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. Google Scholar

[9] H. Hosseinzadeh and V. Parvaneh, Meir-Keeler type contractive mappings in modular and partial modular metric spaces, Asian-European Journal of Mathematics 13 (5) (2020), 2050087. Google Scholar

[10] I.V. Istraescu, Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters-I, Ann. Mat. Pura Appl. 130 (4) (1982), 89–104. Google Scholar

[11] M. Menaka and M. Marudai, Fixed point theorems for weakly generalized w-contraction mappings and applications, International Journal of Mathematics and its Applications, 6 (1-C), (2018), 471–481. Google Scholar

[12] 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. Google Scholar

[13] A.I. Perov, On the Cauchy problem for a system of ordinary differential equations, Pviblizhen, Met.Reshen, Differ. Uvavn. 2 (1964), 115–134. 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. Google Scholar

[15] B. Sam, Jr. Nadler, Multivalued contraction mappings, Pacific Journal Of Mathematics, 30 (2) (1969). Google Scholar