On φ-contractions and fixed point results in fuzzy metric spaces

Morteza Saheli; Seyed Ali Mohammad Mohsenialhosseini; Hadi Saeidi Goraghani

doi:10.4995/agt.2023.17130

Authors

Morteza Saheli Vali Asr University of Rafsanjan https://orcid.org/0000-0002-8368-1598
Seyed Ali Mohammad Mohsenialhosseini Vali Asr University of Rafsanjan https://orcid.org/0000-0002-0166-6184
Hadi Saeidi Goraghani Payame Noor University https://orcid.org/0000-0003-4590-5519

DOI:

https://doi.org/10.4995/agt.2023.17130

Keywords:

φ-contraction, weak φ-contraction, fuzzy metric space, multiple fixed point, comparison function

Abstract

In this paper, φ-contractions are defined and then, some new fixed point theorems are established for certain nonlinear mappings associated with one-dimensional (c)-comparison functions in fuzzy metric spaces. Next, generalized φ-contractions are defined by using five-dimensional (c)-comparison functions, and the existence of fixed points for nonlinear maps on fuzzy metric spaces is studied. Moreover, some examples are given to illustrate our results.

Downloads

Download data is not yet available.

Author Biographies

Morteza Saheli, Vali Asr University of Rafsanjan

Department of Mathematics

Seyed Ali Mohammad Mohsenialhosseini, Vali Asr University of Rafsanjan

Department of Mathematics

Hadi Saeidi Goraghani, Payame Noor University

Department of Mathematics

Department of Mathematics, Vali-e-Asr University of Rafsanjan

References

S. Banach, Sur les operations dans les ensembles abstraits etleur application aux equations integrales, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181

V. Berinde, On the approximation of fixed points of weak contractive mappings, Carpathian J. Math. 19, no. 1 (2003), 7-22.

V. Berinde, Error estimates for approximating fixed points of quasi contractions, General Mathematics 13 (2005), 23-34.

V. Berinde, Iterative approximation of fixed points, Springer-Verlag, Berlin Heidelberg, 2007. https://doi.org/10.1109/SYNASC.2007.49

A. Chitra, and P. V. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Cal. Math. Soc. 74 (1969), 660-665.

J. Franklin, Methods of mathematical economics, Springer Verlag, New York, 1980. https://doi.org/10.1007/978-3-662-25317-5

A. George, and P. Veeramani,On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7

M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4

V. Gregori, and J.-J. Miñana, On fuzzy y-contractive sequences and fixed-point theorems, Fuzzy Sets and Systems 300 (2016), 93-101. https://doi.org/10.1016/j.fss.2015.12.010

V. Gregori, and J.-J. Miñana, Some remarks on fuzzy contractive mappings, Fuzzy Sets and Systems 251 (2014), 101--103. https://doi.org/10.1016/j.fss.2014.01.002

V. Gregori, J. -J. Miñana, and D. Miravet, Contractive sequences in fuzzy metric spaces, Fuzzy Sets and Systems 379 (2020), 125-133. https://doi.org/10.1016/j.fss.2019.01.003

V. Gregori, J. -J. Miñana, and D. Miravet, Extended fuzzy metrics and fixed point theorems, Mathematics 7 (3) (2019), Article 303. https://doi.org/10.3390/math7030303

V. Gregori, J. -J. Miñana, and S. Morillas, On completable fuzzy metric spaces, Fuzzy Sets and Systems 267 (2015), 133-139. https://doi.org/10.1016/j.fss.2014.07.009

V. Gregori, and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9

K. Kramosil, and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), 336-344.

D. Mihet, Erratum to "Fuzzy y-contractive mappings in non-Archimedean fuzzy metric spaces, [Fuzzy Sets and Systems 159 (2008), 739-744]", Fuzzy Sets and Systems 161 (2010), 1150-1151. https://doi.org/10.1016/j.fss.2007.07.006

D. Mihet, Fuzzy y-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159 (2008), 739-744. https://doi.org/10.1016/j.fss.2007.07.006

J. J. Nieto, and R. Rodríguez-López, Contractive mappings theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), 223-239. https://doi.org/10.1007/s11083-005-9018-5

H. K. Pathak, and N. Hussain, Common fixed points for Banach pairs with applications, Nonlinear Anal. 69 (2008), 2788-2802. https://doi.org/10.1016/j.na.2007.08.051

B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290. https://doi.org/10.1090/S0002-9947-1977-0433430-4

S. Shukla, D. Gopal, and W. Sintunavarat, A new class of fuzzy contractive mappings and fixed-point theorems, Fuzzy Sets and Systems 350 (2018), 85-94. https://doi.org/10.1016/j.fss.2018.02.010