×

zbMATH — the first resource for mathematics

Multivalued fixed point theorems for generalized contractions and their applications. (English) Zbl 07037556
Summary: We give common hybrid fixed point results for generalized \((\psi, \phi)\) weak contraction satisfying owc and CLR properties in the framework of metric spaces. An application to functional equations is also discussed.

MSC:
54 General topology
47 Operator theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Gholizadeh, L., A fixed point theorem in generalized ordered metrice spaces with application, The Journal of Nonlinear Science and Applications, 6, 244-251, (2013) · Zbl 1432.54059
[2] Pansuwan, A.; Sintunavarat, W.; Parvaneh, V.; Cho, Y. J., Some fixed point theorems for \(\left(\alpha, \theta, k\right)\)-contraction multi-valued mappings with some applications, Fixed Point Theory and Applications, 2015, article 132, (2015) · Zbl 06583956
[3] Banach, S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3, 1, 133-181, (1922) · JFM 48.0201.01
[4] Alber, Ya. I.; Guerre-Delabriere, S., Principle of weakly contractive maps in hilbert spaces, New Results in Operator Theory and Its Applications: The Israel M. Glazman Memorial Volume. New Results in Operator Theory and Its Applications: The Israel M. Glazman Memorial Volume, Operator Theory: Advances and Applications, 98, 7-22, (1997), Berlin, Germany: Springer, Berlin, Germany · Zbl 0897.47044
[5] Jaggi, D. S., Some unique fixed point theorems, Indian Journal of Pure and Applied Mathematics, 8, 2, 223-230, (1977) · Zbl 0379.54015
[6] Nadler, S. B., Multi-valued contraction mappings, Pacific Journal of Mathematics, 30, 475-488, (1969) · Zbl 0187.45002
[7] Kutbi, M. A.; Sintunavarat, W., Fixed point theorems for generalized \(\omega_\alpha\)-contraction multivalued mappings in αα-complete metric spaces, Fixed Point Theory and Applications, 2014, article 139, (2014) · Zbl 06584157
[8] Shen, M.; Hong, S. H., Common fixed points for generalized contractive multivalued operators in complete metric spaces, Applied Mathematics Letters, 22, 12, 1864-1869, (2009) · Zbl 1203.54047
[9] Rhoades, B. E., Some theorems on weakly contractive maps, Nonlinear Analysis, 47, 4, 2683-2693, (2001) · Zbl 1042.47521
[10] Dutta, P. N.; Choudhury, B. S., A generalisation of contraction principle in metric spaces, Fixed Point Theory and Applications, 2008, (2008) · Zbl 1177.54024
[11] Kutbi, M. A.; Sintunavarat, W., On new fixed point results for \(\left(\alpha, \psi, \xi\right)\)-contractive multi-valued mappings on α-complete metric spaces and theirconsequences, Fixed Point Theory and Applications, 2015, article 2, (2015) · Zbl 1391.54033
[12] Zhang, Q.; Song, Y., Fixed point theory for generalized \(\phi\)-weak contractions, Applied Mathematics Letters, 22, 1, 75-78, (2009) · Zbl 1163.47304
[13] Đorić, D., Common fixed point for generalized \(\left(\psi, \varnothing\right)\)-weak contractions, Applied Mathematics Letters, 22, 12, 1896-1900, (2009) · Zbl 1203.54040
[14] Jungck, G., Commuting mappings and fixed points, The American Mathematical Monthly, 83, 4, 261-263, (1976) · Zbl 0321.54025
[15] Jungck, G., Compatible mappings and common fixed points, International Journal of Mathematics and Mathematical Sciences, 9, 4, 771-779, (1986) · Zbl 0613.54029
[16] Jungck, G.; Rhoades, B. E., Fixed points for set valued functions without continuity, Indian Journal of Pure and Applied Mathematics, 29, 3, 227-238, (1998) · Zbl 0904.54034
[17] Al-Thagafi, M. A.; Shahzad, N., A note on occasionally weakly compatible maps, International Journal of Mathematical Analysis, 3, 1–4, 55-58, (2009) · Zbl 1181.54045
[18] Khan, M. S., Common fixed point theorems for multivalued mappings, Pacific Journal of Mathematics, 95, 2, 337-347, (1981) · Zbl 0419.54030
[19] Singh, S. L.; Ha, K. S.; Cho, Y. J., Coincidence and fixed points of nonlinear hybrid contractions, International Journal of Mathematics and Mathematical Sciences, 12, 2, 247-256, (1989) · Zbl 0669.54024
[20] Singh, S. L.; Mishra, S. N., Nonlinear hybrid contractions, Journal of Natural & Physical Sciences, 5–8, 191-206, (1991–1994) · Zbl 0862.54035
[21] Aliouche, A.; Popa, V., General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications, Novi Sad Journal of Mathematics, 39, 1, 89-109, (2009) · Zbl 1265.54149
[22] Kaneko, H.; Sessa, S., Fixed point theorems for compatible multi-valued and single-valued mappings, International Journal of Mathematics and Mathematical Sciences, 12, 2, 257-262, (1989) · Zbl 0671.54023
[23] Abbas, M.; Rhoades, B. E., Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type, Fixed Point Theory and Applications, 2007, (2007) · Zbl 1153.54307
[24] Aamri, M.; El Moutawakil, D., Some new common fixed point theorems under strict contractive conditions, Journal of Mathematical Analysis and Applications, 270, 1, 181-188, (2002) · Zbl 1008.54030
[25] Sintunavarat, W.; Kumam, P., Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, Journal of Applied Mathematics, 2011, (2011) · Zbl 1226.54061
[26] Abdou, A. A. N., Common fixed point theorems for hybrid contractive pairs with the (CLR)-property, Fixed Point Theory and Applications, 2015, article 138, (2015) · Zbl 06584083
[27] Abdou, A. A., Common fixed point results for multi-valued mappings with some examples, Journal of Nonlinear Science and Its Applications, 9, 3, 787-798, (2016) · Zbl 1437.54034
[28] Roldán, A.; Sintunavarat, W., Common fixed point theorems in fuzzy metric spaces using the CLRg property, Fuzzy Sets and Systems, 282, 131-142, (2016) · Zbl 1392.54034
[29] Liu, Z.-q.; Kang, S. M., Existence and uniqueness of solutions for two classes of functional equations arising in dynamic programming, Acta Mathematicae Applicatae Sinica. English Series, 23, 2, 195-208, (2007) · Zbl 1175.49024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.