Home Fixed fuzzy point results of generalized Suzuki type F-contraction mappings in ordered metric spaces
Article
Licensed
Unlicensed Requires Authentication

Fixed fuzzy point results of generalized Suzuki type F-contraction mappings in ordered metric spaces

  • Naeem Saleem EMAIL logo , Mujahid Abbas and Zahid Raza
Published/Copyright: November 30, 2017
Become an author with De Gruyter Brill

Abstract

The aim of this paper is to introduce generalized Suzuki type F-contraction fuzzy mappings and to prove the existence of fixed fuzzy points for such mappings in the setup of complete ordered metric spaces. An example is provided to show the validity of our results, followed by couple of remarks about the comparison of obtained results with the existing results in the literature. An application of our result to the domain of words is also presented.

MSC 2010: 54H25; 47H10

References

[1] B. Ali and M. Abbas, Suzuki-type fixed point theorem for fuzzy mappings in ordered metric spaces, Fixed Point Theory Appl. 2013 (2013), Paper No. 9. 10.1186/1687-1812-2013-9Search in Google Scholar

[2] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrals, Fund. Math. 3 (1922), 133–181. 10.4064/fm-3-1-133-181Search in Google Scholar

[3] R. Baskaran and P. V. Subrahmanyam, A note on the solution of a class of functional equations, Appl. Anal. 22 (1986), no. 3–4, 235–241. 10.1080/00036818608839621Search in Google Scholar

[4] R. Bellman, Methods of Nonlinear Analysis. , Vol. II, Math. Sci. Eng. 61 Part 2, Academic Press, New York, 1973. Search in Google Scholar

[5] R. Bellman and E. S. Lee, Functional equations in dynamic programming, Aequationes Math. 17 (1978), no. 1, 1–18. 10.1007/BF01818535Search in Google Scholar

[6] P. C. Bhakta and S. Mitra, Some existence theorems for functional equations arising in dynamic programming, J. Math. Anal. Appl. 98 (1984), no. 2, 348–362. 10.1016/0022-247X(84)90254-3Search in Google Scholar

[7] S.-S. Chang, Fixed degree for fuzzy mappings and a generalization of Ky Fan’s theorem, Fuzzy Sets and Systems 24 (1987), no. 1, 103–112. 10.1016/0165-0114(87)90118-7Search in Google Scholar

[8] V. D. Estruch and A. Vidal, A note on fixed fuzzy points for fuzzy mappings, Rend. Istit. Mat. Univ. Trieste 32 (2001), 39–45. Search in Google Scholar

[9] P. Flajolet, Analytic analysis of algorithms, Automata, Languages and Programming (Vienna 1992), Lecture Notes in Comput. Sci. 623, Springer, Berlin (1992), 186–210. 10.1007/3-540-55719-9_74Search in Google Scholar

[10] R. H. Haghi, S. Rezapour and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal. 74 (2011), no. 5, 1799–1803. 10.1016/j.na.2010.10.052Search in Google Scholar

[11] S. Heilpern, Fuzzy mappings and fixed point theorem, J. Math. Anal. Appl. 83 (1981), no. 2, 566–569. 10.1016/0022-247X(81)90141-4Search in Google Scholar

[12] M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008), no. 9, 2942–2949. 10.1016/j.na.2007.08.064Search in Google Scholar

[13] D. Klim and D. Wardowski, Fixed points of dynamic processes of set-valued F-contractions and application to functional equations, Fixed Point Theory Appl. 2015 (2015), Paper No. 22. 10.1186/s13663-015-0272-ySearch in Google Scholar

[14] R. L. Kruse, Data Structures and Program Design, Prentice-Hall, Upper Saddle River, 1987. Search in Google Scholar

[15] B. S. Lee and S. J. Cho, A fixed point theorem for contractive-type fuzzy mappings, Fuzzy Sets and Systems 61 (1994), no. 3, 309–312. 10.1016/0165-0114(94)90173-2Search in Google Scholar

[16] S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475–488. 10.2140/pjm.1969.30.475Search in Google Scholar

[17] J. J. Nieto, R. L. Pouso and R. Rodríguez-López, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc. 135 (2007), no. 8, 2505–2517. 10.1090/S0002-9939-07-08729-1Search in Google Scholar

[18] J. J. Nieto and R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), no. 3, 223–239. 10.1007/s11083-005-9018-5Search in Google Scholar

[19] J. J. Nieto and R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 12, 2205–2212. 10.1007/s10114-005-0769-0Search in Google Scholar

[20] D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl. 159 (2012), no. 3, 911–920. 10.1016/j.topol.2011.12.008Search in Google Scholar

[21] A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435–1443. 10.1090/S0002-9939-03-07220-4Search in Google Scholar

[22] S. Romaguera, A. Sapena and P. Tirado, The Banach fixed point theorem in fuzzy quasi-metric spaces with application to the domain of words, Topology Appl. 154 (2007), no. 10, 2196–2203. 10.1016/j.topol.2006.09.018Search in Google Scholar

[23] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), Paper No. 94. 10.1186/1687-1812-2012-94Search in Google Scholar

[24] L. A. Zadeh, Fuzzy sets, Inf. Control 8 (1965), 338–353. 10.21236/AD0608981Search in Google Scholar

Received: 2015-10-26
Accepted: 2016-09-22
Published Online: 2017-11-30
Published in Print: 2020-06-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 1.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/gmj-2017-0048/html
Scroll to top button