Fuzzy endpoint results for ´ Ciri´c-generalized quasicontractive fuzzy mappings

Iranian Journal of Numerical Analysis and Optimization

مقاله 10، دوره 9، شماره 2 - شماره پیاپی 16، دی 2019، صفحه 185-191   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v9i2.63018

نویسنده

B. Mohammadi^*

Islamic Azad University, Marand

چکیده

We introduce Ciri´c-generalized quasicontractive fuzzy mappings and pro vide the necessary and sufficient conditions of having a unique endpoint for such mappings. Then we introduce β-ψ-quasicontractive fuzzy mappings, es tablishing an endpoint result for them. Finally, we provide some results as an application.

کلیدواژه‌ها

Fuzzy endpoint, \'{C}iri\'{c}-generalized؛ quasicontractive fuzzy mappings؛ approximate endpoint property‎

مراجع

1. Abbas, M., Turkoglu, D. Fixed point theorem for a generalized contractive fuzzy mapping, J. Intell. Fuzzy Systems. 26 (2014), 33–36.

2. Amini-Harandi, A. Endpoints of set-valued contractions in metric spaces, Nonlinear Anal. 72 (2010), 132–134.

3. Azam, A., Beg, I. Common fixed points of fuzzy maps, Math. Comput. Modelling. 49 (2009), 1331–1336.

4. Ciri´c, L.B. ´ A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267–273.

5. Estruch, V.D., Vidal, A. A note on fixed fuzzy points for fuzzy mappings, Rend Istit. Mat. Univ. Trieste. 32 (2001), 39-45.

6. Heilpern, S. Fuzzy mappings and fixed point theorems, J. Math. Anal. Appl. 83 (1981), 566–569.

7. Mohammadi, B., Rezapour, SH., Shahzad, N. Some results on fixed points of α-ψ-Ciric generalized multifunctions, Fixed Point Theory Appl. (2013):24.

8. Moradi, S., Khojasteh, F. Endpoints of multi-valued generalized weak con traction mappings, Nonlinear Anal. 74 (2011), 2170–2174.

9. Nadler, S.B. Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475–488.

10. Samet, B., Vetro, C., Vetro, P. Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154–2165.

11. Turkoglu, D., Rhoades, B.E. A fixed fuzzy point for fuzzy mapping in complete metric spaces, Math. Commun. 10 (2005), 115–121.

12. Zadeh, L.A. Fuzzy sets, Inf. Control. 8 (1965), 103–112.