Korean J. Math. Vol. 27 No. 4 (2019) pp.861-877
DOI: https://doi.org/10.11568/kjm.2019.27.4.861

Fixed point theorems for asymptotically regular mappings in fuzzy metric spaces

Main Article Content

Nilakshi Goswami
Bijoy Patir


The aim of this paper is to extend some existing fixed point results for asymptotically regular mappings to fuzzy metric spaces. For this purpose some contractive type conditions with respect to an altering distance function are used. Some new common fixed point results have been derived for such mappings. We provide suitable examples to justify our study.

Article Details


[1] F. E Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach Spaces, Bull. Amer. Math. Soc.72, 571-575 (1966). Google Scholar

[2] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Set. Syst. 64, 395-399 (1994). Google Scholar

[3] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Set. Syst. 27, 385-389 (1988). Google Scholar

[4] A. A. Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary different equations, Nonlinear Analysis 72, 2238-2242 (2010). Google Scholar

[5] M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30, 1-9 (1984). Google Scholar

[6] B. E. Rhoades, S. Seesa, M. S. Khan, M. D. Khan , Some fixed point theorems for hardy-rogers type mappings, International J. Math. and Math. Sci. 7, 75-87 (1984). Google Scholar

[7] J. Rodriguez-Lopez, S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets Syst. 147, 273-283 (2004). Google Scholar

[8] H. K. Nashine, Z. Kadelburg, Common fixed point theorems for asymptotically regular mappings on ordered orbitally complete metric spaces with an application to systems of integral equations, Filomat 30:12, 3277-3289 (2016). Google Scholar

[9] P. Nigam and S. S. Pagey, Some fixed point theorems for a pair of asymptotically regular and compatible mappings in fuzzy 2-metric space, Int. J. Open Problems Comput. Math., 5(1), 71-84 (2012). Google Scholar

[10] B. Patir, N. Goswami, L. N. Mishra, Fixed point theorems in fuzzy metric spaces for mappings with some contractive type conditions, Korean J. Math., 26 (2), 307-326 (2018). Google Scholar

[11] B. Patir, N. Goswami, V. N. Mishra, Some results on fixed point theory for a class of generalized nonexpansive mappings, Fixed Point Theory and Applications 2018:19 (2018). Google Scholar

[12] K. Prudhvi, A common fixed point theorem for asymptotically regular in cone metric spaces, Asian Journal of Fuzzy and Applied Mathematics 2(1), 12-16 (2014). Google Scholar

[13] K. P. R. Sastry, V. S. R. Naidu, I. H. N. Rao, K. P. R. Rao, Common fixed points for asymptotically regular mappings, Indian J. Pure Appl. Math., 15(8), 849-854 (1984). Google Scholar

[14] Y. Shen, D. Qiu, W. Chen, Fixed point theorems in fuzzy metric spaces, Appl. Math. Lett. 25, 138-141 (2012). Google Scholar

[15] S. Shukla, I. Altun, R. Sen, Fixed point theorems and asymptotically regular mappings in partial metric spaces, ISRN Computational Mathematics 2013, 6 pages (2013). Google Scholar

[16] B. C. Tripathy, S. Paul, N. R. Das, A fixed point theorem in a generalized fuzzy metric space, Bol. Soc. Paran. Mat., 32(2), 221-227 (2014). Google Scholar