Fuzzy \((h,\beta )\)-contractions in non-Archimedean fuzzy metric spaces. (English) Zbl 1477.54146
Summary: In this work, we introduce the new concepts of fuzzy \((h,\beta )\)-contractive mapping via triangular \((h,\beta ) \)-admissible mappings. Later, we prove some fixed point results for some mappings that provide fuzzy \((h,\beta )\)-contractibility and triangular \((h,\beta ) \)-admissibility in complete non-Archimedean fuzzy metric spaces. Some examples are supplied in order to support the usability of our results. Our main results substantially generalize and extend some known results in the existing literature.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54A40 | Fuzzy topology |
| 54E40 | Special maps on metric spaces |
Keywords:
triangular \((h, \beta )\)-admissible mapping; fuzzy \((h, \beta )\)-contractive mapping; fixed point; fuzzy metricReferences:
| [1] | Altun, I., and Mihet¸, D.Ordered non-Archimedean fuzzy metric spaces and some fixed point results.Fixed Point Theory Appl.(2010), Art. ID 782680, 11. · Zbl 1191.54033 |
| [2] | Banach, S.Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales.Fund. Math. 3(1922), 133-181. · JFM 48.0201.01 |
| [3] | Chauhan, S., Bhatnagar, S., and Radenovi´c, S.Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces.Matematiche (Catania) 68, 1 (2013), 87-98. · Zbl 1282.54035 |
| [4] | Chauhan, S., Pant, B. D., and Imdad, M.Coincidence and common fixed point theorems in non-Archimedean Menger PM-spaces.Cubo 15, 3 (2013), 31-44. · Zbl 1295.54045 |
| [5] | Deng, Z.Fuzzy pseudometric spaces.J. Math. Anal. Appl. 86, 1 (1982), 74-95. · Zbl 0501.54003 |
| [6] | Di Bari, C., and Vetro, C.Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space.J. Fuzzy Math. 13, 4 (2005), 973-982. · Zbl 1102.54001 |
| [7] | Dinarvand, M.Some fixed point results for admissible Geraghty contraction type mappings in fuzzy metric spaces.Iran. J. Fuzzy Syst. 14, 3 (2017), 161-177, 191. · Zbl 1398.54067 |
| [8] | George, A., and Veeramani, P.On some results in fuzzy metric spaces. Fuzzy Sets and Systems 64, 3 (1994), 395-399. · Zbl 0843.54014 |
| [9] | Grabiec, M.Fixed points in fuzzy metric spaces.Fuzzy Sets and Systems 27, 3 (1988), 385-389. · Zbl 0664.54032 |
| [10] | Gregori, V., and Sapena, A.On fixed-point theorems in fuzzy metric spaces. Fuzzy Sets and Systems 125, 2 (2002), 245-252. · Zbl 0995.54046 |
| [11] | Isik, H., Samet, B., and Vetro, C.Cyclic admissible contraction and applications to functional equations in dynamic programming.Fixed Point Theory Appl.(2015), 2015:163, 19. · Zbl 1470.54067 |
| [12] | Istr˘at¸escu, V.An Introduction to Theory of Probabilistic Metric Spaces, with Applications. Ed, Tehnic˘a. Bucure¸sti, in Romanian, 1974. |
| [13] | Jungck, G., and Rhoades, B. E.Fixed points for set valued functions without continuity.Indian J. Pure Appl. Math. 29, 3 (1998), 227-238. · Zbl 0904.54034 |
| [14] | Kramosil, I., and Mich´alek, J.Fuzzy metrics and statistical metric spaces. Kybernetika (Prague) 11, 5 (1975), 336-344. · Zbl 0319.54002 |
| [15] | Mihet¸, D.On fuzzy contractive mappings in fuzzy metric spaces.Fuzzy Sets and Systems 158, 8 (2007), 915-921. · Zbl 1117.54008 |
| [16] | Mihet¸, D.Fuzzyψ-contractive mappings in non-Archimedean fuzzy metric spaces.Fuzzy Sets and Systems 159, 6 (2008), 739-744. · Zbl 1171.54330 |
| [17] | Radenovi´c, S.Classical fixed point results in 0-complete partial metric spaces via cyclic-type extension.Bull. Allahabad Math. Soc. 31, 1 (2016), 39-55. · Zbl 06651316 |
| [18] | Radenovi´c, S.Some remarks on mappings satisfying cyclical contractive conditions.Afr. Mat. 27, 1-2 (2016), 291-295. · Zbl 1338.54209 |
| [19] | Salimi, P., Vetro, C., and Vetro, P.Some new fixed point results in nonArchimedean fuzzy metric spaces.Nonlinear Anal. Model. Control 18, 3 (2013), 344-358. · Zbl 1305.54057 |
| [20] | Samet, B., Vetro, C., and Vetro, P.Fixed point theorems forα-ψcontractive type mappings.Nonlinear Anal. 75, 4 (2012), 2154-2165. · Zbl 1242.54027 |
| [21] | Sangurlu, M., and Turkoglu, D.Fixed point theorems for (ψ◦ϕ)— contractions in a fuzzy metric spaces.J. Nonlinear Sci. Appl. 8, 5 (2015), 687-694. · Zbl 1328.54048 |
| [22] | Schweizer, B., and Sklar, A.Statistical metric spaces.Pacific J. Math. 10 (1960), 313-334. · Zbl 0091.29801 |
| [23] | Schweizer, B., and Sklar, A.Probabilistic Metric Spaces. North-Holland, Amsterdam, 1983. · Zbl 0546.60010 |
| [24] | Sedghi, S., Shobkolaei, N., Doˇsenovi´c, T., and Radenovi´c, S.Suzukitype of common fixed point theorems in fuzzy metric spaces.Math. Slovaca 68, 2 (2018), 451-462. · Zbl 1505.54091 |
| [25] | Shen, Y. H., Qiu, D., and Chen, W.Fixed point theory for cyclicφcontractions in fuzzy metric spaces.Iran. J. Fuzzy Syst. 10, 4 (2013), 125-133, 153. · Zbl 1333.54050 |
| [26] | Turkoglu, D., and Sangurlu, M.Fixed point theorems for fuzzyψcontractive mappings in fuzzy metric spaces.J. Intell. Fuzzy Systems 26, 1 (2014), 137-142. · Zbl 1308.54039 |
| [27] | Vasuki, R., and Veeramani, P.Fixed point theorems and Cauchy sequences in fuzzy metric spaces.Fuzzy Sets and Systems 135, 3 (2003), 415-417. · Zbl 1029.54012 |
| [28] | Vetro, C.Fixed points in weak non-Archimedean fuzzy metric spaces.Fuzzy Sets and Systems 162(2011), 84-90. · Zbl 1206.54066 |
| [29] | Vetro, C., Gopal, D., and Imdad, M.Common fixed point theorems for (φ, ψ)-weak contractions in fuzzy metric spaces.Indian J. Math. 52, 3 (2010), 573-590 · Zbl 1217.54059 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
