Fuzzy fixed point results of generalized almost F-contraction

Authors

Abdullah Eqal Al-Mazrooei - Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia
Jamshaid Ahmad - Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia

Abstract

The aim of this paper is to obtain some common \(\alpha \)-fuzzy fixed points for fuzzy mappings under almost \(F\)-contraction in the setting of metric space. In this way we generalize, unify, and complement fuzzy fixed point results of literature. As an application, we derive some multivalued fixed point theorems as a direct consequence of our main results. We also provide a non trivial example to show the significance of the investigation of this paper.

Keywords

\(\alpha \)-Fuzzy fixed points, \(F\)-contraction, multivalued mapping, metric space

References

[1] H. M. Abu-Donia, Common fixed point theorems for fuzzy mappings in metric space under \(\phi\)-contraction condition, Chaos Solitons Fractals, 34 (2007), 538–543.
[2] H. Adibi, Y. J. Cho, D. O’Regan, R. Saadati, Common fixed point theorems in L-fuzzy metric spaces, Appl. Math. Comput., 182 (2006), 820–828.
[3] J. Ahmad, A. Al-Rawashdeh, A. Azam, Fixed point results for \(\{\alpha,\xi\}\)-expansive locally contractive mappings, J. Inequal. Appl., 2014 (2014), 10 pages.
[4] J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized F-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 18 pages.
[5] A. Al-Rawashdeh, J. Ahmad, Common fixed point theorems for JS-contractions, Bull. Math. Anal. Appl., 8 (2016), 12–22.
[6] I. Altun, G. Durmaz, G. Mınak, S. Romaguera, Multivalued almost F-contractions on complete metric spaces, Filomat, 30 (2016), 441–448.
[7] I. Altun, G. Minak, H. Dağ, Multivalued F-contractions on complete metric spaces, J. Nonlinear Convex Anal., 16 (2015), 659–666.
[8] S. C. Arora, V. Sharma, Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems, 110 (2000), 127–130.
[9] Z. Aslam, J. Ahmad, N. Sultana, New common fixed point theorems for cyclic compatible contractions, J. Math. Anal., 8 (2017), 1–12.
[10] A. Azam, M. Arshad, P. Vetro, On a pair of fuzzy \(\phi\)-contractive mappings, Math. Comput. Modelling, 52 (2010), 207–214.
[11] A. Azam, I. Beg, Common fixed points of fuzzy maps, Math. Comput. Modelling, 49 (2009), 1331–1336.
[12] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181.
[13] V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9 (2004), 43–53.
[14] V. Berinde, General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces, Carpathian J. Math., 24 (2008), 10–19.
[15] R. K. Bose, D. Sahani, Fuzzy mappings and fixed point theorems, Fuzzy Sets and Systems, 21 (1987), 53–58.
[16] S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung, S. M. Kang, Coincidence point theorems and minimization theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 88 (1997), 119–127.
[17] Y. J. Cho, N. Petrot, Existence theorems for fixed fuzzy points with closed -cut sets in complete metric spaces, Commun. Korean Math. Soc., 26 (2011), 115–124.
[18] S. Heilpern, Fuzzy mappings and fixed point theorem, J. Math. Anal. Appl., 83 (1981), 566–569.
[19] A. Hussain, New approach of F-contraction involving fixed point on a closed ball, Turkish J. Anal. Number Theory, 4 (2016), 159–163.
[20] N. Hussain, J. Ahmad, A. Azam, On Suzuki-Wardowski type fixed point theorems, J. Nonlinear Sci. Appl., 8 (2015), 1095–1111.
[21] N. Hussain, A. E. Al-Mazrooei, J. Ahmad, Fixed point results for generalized \((\alpha-\eta)-\Theta\) contractions with applications, J. Nonlinear Sci. Appl., 10 (2017), 4197–4208.
[22] S. U. Khan, M. Arshad, A. Hussain, M. Nazam, Two new types of fixed point theorems for F-contraction, J. Adv. Stud. Topol., 7 (2016), 251–260.
[23] G. Minak, I. Altun, S. Romaguera, Recent developments about multivalued weakly Picard operators, Bull. Belg. Math. Soc. Simon Stevin, 22 (2015), 411–422.
[24] S. B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475–478.
[25] D. Qiu, L. Shu, Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings, Inform. Sci., 178 (2008), 3595–3604.
[26] R. A. Rashwan, M. A. Ahmed, Common fixed point theorems for fuzzy mappings, Arch. Math. (Brno), 38 (2002), 219–226.
[27] R. Saadati, S. M. Vaezpour, Y. J. Cho, Quicksort algorithm: application of a fixed point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words, J. Comput. Appl. Math., 228 (2009), 219–225.
[28] N. A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl., 2013 (2013), 13 pages.
[29] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 6 pages.
[30] S.-S. Zhang, Fixed point theorems for fuzzy mappings, II, (Chinese) ; translated from Appl. Math. Mech., 7 (1986), 133–138, Appl. Math. Mech. (English Ed.), 7 (1986), 147–152.

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