Fixed Point Theorems Related to Fuzzy Metric Spaces

In the present paper some fixed point and common fixed point theorems in complete Fuzzy 2-metric spaces and fuzzy 3- metric spaces are established which are motivated by Gahler [13-15], Sharma, Sharma and Isekey [30],Sharma , S.[31], Key Words: Fuzzy metric spaces, fuzzy 2- metric spaces, fuzzy 3- metric spaces fixed point, Common fixed point

Fixed Point Theorems in Random Fuzzy Metric Space

In the present paper some fixed point theorems in complete RandomFuzzy metric spaces are established which are generalizations of fuzzy metric spaces for various type mappings. Key Words: Fuzzy metric spaces, Random fuzzy metric spaces, fixed point , Common fixed point . AMS Subject classification 47H10, 54H2

w-Distances on Fuzzy Metric Spaces and Fixed Points

[EN] We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi.Romaguera Bonilla, S. (2020). w-Distances on Fuzzy Metric Spaces and Fixed Points. Mathematics. 8(11):1-9. https://doi.org/10.3390/math8111909S19811Suzuki, T., & Takahashi, W. (1996). Fixed point theorems and characterizations of metric completeness. Topological Methods in Nonlinear Analysis, 8(2), 371. doi:10.12775/tmna.1996.040Suzuki, T. (2001). Generalized Distance and Existence Theorems in Complete Metric Spaces. Journal of Mathematical Analysis and Applications, 253(2), 440-458. doi:10.1006/jmaa.2000.7151Al-Homidan, S., Ansari, Q. H., & Yao, J.-C. (2008). Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory. Nonlinear Analysis: Theory, Methods & Applications, 69(1), 126-139. doi:10.1016/j.na.2007.05.004Lakzian, H., & Lin, I.-J. (2012). The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with -Distances. Journal of Applied Mathematics, 2012, 1-11. doi:10.1155/2012/161470Alegre, C., Marín, J., & Romaguera, S. (2014). A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces. Fixed Point Theory and Applications, 2014(1). doi:10.1186/1687-1812-2014-40Alegre, C., & Marín, J. (2016). Modified w-distances on quasi-metric spaces and a fixed point theorem on complete quasi-metric spaces. Topology and its Applications, 203, 32-41. doi:10.1016/j.topol.2015.12.073Lakzian, H., Rakočević, V., & Aydi, H. (2019). Extensions of Kannan contraction via w-distances. Aequationes mathematicae, 93(6), 1231-1244. doi:10.1007/s00010-019-00673-6Alegre, C., Fulga, A., Karapinar, E., & Tirado, P. (2020). A Discussion on p-Geraghty Contraction on mw-Quasi-Metric Spaces. Mathematics, 8(9), 1437. doi:10.3390/math8091437Abbas, M., Ali, B., & Romaguera, S. (2015). Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness. Filomat, 29(6), 1217-1222. doi:10.2298/fil1506217aRomaguera, S., & Tirado, P. (2020). Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results. Mathematics, 8(2), 273. doi:10.3390/math8020273Kirk, W. A. (1976). Caristi’s fixed point theorem and metric convexity. Colloquium Mathematicum, 36(1), 81-86. doi:10.4064/cm-36-1-81-86Hu, T. K. (1967). On a Fixed-Point Theorem for Metric Spaces. The American Mathematical Monthly, 74(4), 436. doi:10.2307/2314587Subrahmanyam, P. V. (1975). Completeness and fixed-points. Monatshefte f�r Mathematik, 80(4), 325-330. doi:10.1007/bf01472580Grabiec, M. (1988). Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems, 27(3), 385-389. doi:10.1016/0165-0114(88)90064-4Radu, V. (1987). Some fixed point theorems probabilistic metric spaces. Lecture Notes in Mathematics, 125-133. doi:10.1007/bfb0072718Riaz, M., & Hashmi, M. R. (2018). Fixed points of fuzzy neutrosophic soft mapping with decision-making. Fixed Point Theory and Applications, 2018(1). doi:10.1186/s13663-018-0632-5Riaz, M., & Hashmi, M. R. (2019). Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems. Journal of Intelligent & Fuzzy Systems, 37(4), 5417-5439. doi:10.3233/jifs-190550Hashmi, M. R., & Riaz, M. (2020). A novel approach to censuses process by using Pythagorean m-polar fuzzy Dombi’s aggregation operators. Journal of Intelligent & Fuzzy Systems, 38(2), 1977-1995. doi:10.3233/jifs-19061

On some triangular inequalities and applications in 2-fuzzy metric spaces

The aim of this paper is to study some level forms of triangular inequality of 2-fuzzy metric spaces which will be useful for application to fixed point problems. For this aim, we first define the concept of 2-fuzzy pre-metric spaces that have weaker axioms than 2-fuzzy metric spaces with the fundamental properties. Then, we investigate the level form inequalities in 2-fuzzy metric spaces equvalent to the triangular inequalities of 2-fuzzy metric spaces by also analyzing the conditions under in which these are provided. Finally, we prove a fixed point theorem for 2-fuzzy metric spaces by considering the obtained level forms of triangular inequalities.Publisher's Versio

Common Fixed Point of Occasionally Weakly Compatible Maps on Intuitionistic Fuzzy Metric Spaces For Integral Type Inequality

In this paper, We obtain common fixed point theorems in intuitionistic fuzzy metric spaces using Occasionally weakly compatible maps for integral type inequality. Our results are the intuitionistic fuzzy version of some fixed point theorems for weakly compatible mappings on different metric spaces. Key words and phrases: Intuitionistic fuzzy metric space, Occasionally weakly Compatible mappings, Common fixed point

Common Fixed Point Theorem for Occasionally Weakly Compatible Mapping in Q-Fuzzy Metric Spaces

This Paper present some common fixed point theorem for Occasionally Weakly Compatible mapping in Q-fuzzy metric spaces under various conditions. Keywords: Fixed point , Occasionally Weakly Compatible  mapping,  Q-fuzzy metric spaces , t-nor

On completeness in metric spaces and fixed point theorems

[EN] Complete ultrametric spaces constitute a particular class of the so called, recently, G-complete metric spaces. In this paper we characterize a more general class called weak G-complete metric spaces, by means of nested sequences of closed sets. Then, we also state a general fixed point theorem for a self-mapping of a weak G-complete metric space. As a corollary, every asymptotically regular self-mapping of a weak G-Complete metric space has a fixed point.V. Gregori acknowledges the support of the Ministry of Economy and Competitiveness of Spain under Grant MTM2015-64373-P (MINECO/Feder, UE). J.J. Minana acknowledges financial support from the Spanish Ministry of Economy and Competitiveness under Grants TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE funds, by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by Project Ref. PROCOE/4/2017 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears), and by project ROBINS. The latter has received research funding from the EU H2020 framework under GA 779776. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.Gregori Gregori, V.; Miñana, J.; Roig, B.; Sapena Piera, A. (2018). On completeness in metric spaces and fixed point theorems. Results in Mathematics. 73(4):1-13. https://doi.org/10.1007/s00025-018-0896-4113734Bourbaki, N.: Topologie Générale II. Herman, Paris (1974)Boyd, D.W., Wong, J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–469 (1969)Browder, F.E., Petryshyn, W.V.: The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Am. Math. Soc. 72, 571–575 (1966)Edelstein, M.: On fixed and periodic points under contractive mappings. J. Lond. Math. Soc. 37, 74–79 (1962)Fang, J.X.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46(1), 107–113 (1992)Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1989)Gregori, V., Sapena, A.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 125, 245–252 (2002)Gregori, V., Miñana, J.-J., Morillas, S., Sapena, A.: Cauchyness and convergence in fuzzy metric spaces. RACSAM 111(1), 25–37 (2017)Gregori, V., Miñana, J-J., Sapena, A.: On Banach contraction principles in fuzzy metric spaces. Fixed Point Theory (to appear)Kelley, J.: General Topology. Van Nostrand, Princeton (1955)Matkowski, J.: Integrable solutions of functional equations. Dissertationes Mathematicae (Rozprawy Matematyczne) 127, 1–63 (1975)Mihet, D.: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 8431–439 (2004)Steen, L.A., Seebach, J.A.: Counterexamples in Topology, 2nd edn. Springer, Berlin (1978)Tirado, P.: On compactness and G-completeness in fuzzy metric spaces. Iran. J. Fuzzy Syst. 9(4), 151–158 (2012)Tirado, P.: Contraction mappings in fuzzy quasimetric spaces and $$[0,1]$$ [ 0 , 1 ] -fuzzy posets. Fixed Point Theory 13(1), 273–283 (2012)Vasuki, R., Veeramani, P.: Fixed points theorems and Cauchy sequences in fuzzy metric spaces. Fuzzy Sets Syst. 135(3), 415–417 (2003

Fixed points for fuzzy quasi-contractions in fuzzy metric spaces endowed with a graph

[EN] In this paper, we introduce the notion of G-fuzzy H-quasi-contractions using directed graphs in the setting of fuzzy metric spaces endowed with a graph and we show that this new type of contraction generalizes a large number of different types of contractions. Subsequently, we investigate some results concerning the existence of fixed points for this class of contractions under two different conditions in M-complete fuzzy metric spaces endowed with a graph. Our main results of the work significantly generalize many known comparable results in the existing literature. Examples are given to support the usability of our results and to show that they are improvements of some known ones.Dinarvand, M. (2020). Fixed points for fuzzy quasi-contractions in fuzzy metric spaces endowed with a graph. Applied General Topology. 21(2):177-194. https://doi.org/10.4995/agt.2020.11369OJS177194212S. M. A. Aleomraninejad, Sh. Rezapour and N. Shahzad, Some fixed point results on a metric space with a graph, Topology Appl. 159, no. 3 (2012), 659-663. https://doi.org/10.1016/j.topol.2011.10.013A. Amini-Harandi and D. Mihet, Quasi-contractive mappings in fuzzy metric spaces, Iranian J. Fuzzy Syst. 12, no. 4 (2015), 147-153.F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. Stiint. Univ. ''Ovidius" Constanta Ser. Mat. 20, no. 1 (2012), 31-40. https://doi.org/10.2478/v10309-012-0003-xF. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal. 75 (2012), 3895-3901. https://doi.org/10.1016/j.na.2012.02.009J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976. https://doi.org/10.1007/978-1-349-03521-2S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. 25 (1972), 727-730.Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45, no. 2 (1974), 267-273. https://doi.org/10.2307/2040075M. Dinarvand, Fixed point results for $(varphi,psi)$-contractions in metric spaces endowed with a graph, Mat. Vesn. 69, no. 1 (2017), 23-38.M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets Syst. 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canadian Math. Bull. 16 (1973), 201-206. https://doi.org/10.4153/CMB-1973-036-0J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 136, no. 4 (2008), 1359-1373. https://doi.org/10.1090/S0002-9939-07-09110-1R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71-76. https://doi.org/10.2307/2316437I. Kramosil and J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetica 11, no. 5 (1975), 336-344.A. Petrusel and I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134, no. 2 (2006), 411-418. https://doi.org/10.1090/S0002-9939-05-07982-7S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. 5 (1972), 26-42.B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290. https://doi.org/10.1090/S0002-9947-1977-0433430-4S. Shukla, Fixed point theorems of G-fuzzy contractions in fuzzy metric spaces endowed with a graph, Commun. Math. 22 (2014), 1-12. https://doi.org/10.1186/1687-1812-2014-127D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222 (2013), 108-114. https://doi.org/10.1016/j.fss.2013.01.012L. A. Zadeh, Fuzzy Sets, Inform. Control, 10, no. 1 (1960), 385-389

The periodic points of ε-contractive maps in fuzzy metric spaces

[EN] In this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points of f. Furthermore, we present two examples to illustrate the applicability of the obtained results.Project supported by NNSF of China (11761011) and NSF of Guangxi (2020GXNSFAA297010) and PYMRBAP for Guangxi CU(2021KY0651)Sun, T.; Han, C.; Su, G.; Qin, B.; Li, L. (2021). The periodic points of ε-contractive maps in fuzzy metric spaces. Applied General Topology. 22(2):311-319. https://doi.org/10.4995/agt.2021.14449OJS311319222M. Abbas, M. Imdad and D. Gopal, ψ-weak contractions in fuzzy metric spaces, Iranian J. Fuzzy Syst. 8 (2011), 141-148.I. Beg, C. Vetro, D, Gopal and M. Imdad, (Φ, ψ)-weak contractions in intuitionistic fuzzy metric spaces, J. Intel. Fuzzy Syst. 26 (2014), 2497-2504. https://doi.org/10.3233/IFS-130920A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1989), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4V. Gregori and J. J. Miñana, Some remarks on fuzzy contractive mappings, Fuzzy Sets Syst. 251 (2014), 101-103. https://doi.org/10.1016/j.fss.2014.01.002V. Gregori and J. J. Miñana, On fuzzy $Psi$-contractive sequences and fixed point theorems, Fuzzy Sets Syst. 300 (2016), 93-101. https://doi.org/10.1016/j.fss.2015.12.010V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets Syst. 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9J. Harjani, B. López and K. Sadarangani, Fixed point theorems for cyclic weak contractions in compact metric spaces, J. Nonl. Sci. Appl. 6 (2013), 279-284. https://doi.org/10.22436/jnsa.006.04.05X. Hu, Z. Mo and Y. Zhen, On compactnesses of fuzzy metric spaces (Chinese), J. Sichuan Norm. Univer. (Natur. Sei.) 32 (2009), 184-187.I. Kramosil and J. Michàlek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), 336-344.D. Mihet, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets Sys. 159 (2008), 739-744. https://doi.org/10.1016/j.fss.2007.07.006D. Mihet, A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets Syst. 251 (2014), 83-91. https://doi.org/10.1016/j.fss.2014.04.010B. Schweizer and A. Sklar, Statistical metrics paces, Pacif. J. Math. 10 (1960), 385-389. https://doi.org/10.2140/pjm.1960.10.313Y. Shen, D. Qiu and W. Chen, Fixed point theorems in fuzzy metric spaces, Appl. Math. Letters 25 (2012), 138-141. https://doi.org/10.1016/j.aml.2011.08.002S. Shukla, D. Gopal and A. F. Roldán-López-de-Hierro, Some fixed point theorems in 1-M-complete fuzzy metric-like spaces, Inter. J. General Syst. 45 (2016), 815-829. https://doi.org/10.1080/03081079.2016.1153084S. Shukla, D. Gopal and W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets Syst. 359 (2018), 85-94. https://doi.org/10.1016/j.fss.2018.02.010D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222 (2013), 108-114. https://doi.org/10.1016/j.fss.2013.01.012D. Zheng and P. Wang, On probabilistic Ψ-contractions in Menger probabilistic metric spaces, Fuzzy Sets Syst. 350 (2018), 107-110. https://doi.org/10.1016/j.fss.2018.02.011D. Zheng and P. Wang, Meir-Keeler theorems in fuzzy metric spaces, Fuzzy Sets Syst. 370 (2019), 120-128. https://doi.org/10.1016/j.fss.2018.08.01