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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
Full Text:
##### 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
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