×

Common fixed point theorem for hybrid generalized multi-valued contraction mappings. (English) Zbl 1231.54029

Summary: We introduce the notion of a hybrid generalized multi-valued contraction mapping and establish a common fixed point theorem for these mappings. Our results generalize, unify, extend and complement several common fixed point theorems of many authors in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Banach, S., Sur LES opérations dans LES ensembles abstraits et leurs applications aux équations intégrales, Fund. math., 3, 133-181, (1922) · JFM 48.0201.01
[2] Nadler, S.B., Multivalued contraction mappings, Pacific J. math., 475-488, (1969) · Zbl 0187.45002
[3] Markin, J.T., Continuous dependence of fixed point sets, Proc. amer. math. soc., 38, 545-547, (1973) · Zbl 0278.47036
[4] Daffer, P.Z.; Kaneko, H., Fixed points of generalized contractive multi-valued mappings, J. math. anal. appl., 192, 655-666, (1995) · Zbl 0835.54028
[5] Mizoguchi, N.; Takahashi, W., Fixed point theorems for multi-valued mappings on complete metric space, J. math. anal. appl., 141, 177-188, (1989) · Zbl 0688.54028
[6] Mongkolkeha, C.; Kumam, P., Fixed point and common fixed point theorems for generalized weak contraction mappings of integral type in modular spaces, Int. J. math. math. sci., 2011, (2011), Article ID 705943, 12 pages · Zbl 1221.47102
[7] Petrusel, A., On frigon granas-type multifunctions, Nonlinear anal. forum, 7, 113-121, (2002) · Zbl 1043.47036
[8] Reich, S., A fixed point theorem for locally contractive multi-valued functions, Rev. roumaine math. pures appl., 17, 569-572, (1972) · Zbl 0239.54033
[9] Rus, I.A.; Petrusel, A.; Sintamarian, A., Data dependence of fixed point set of some multi-valued weakly Picard operators, Nonlinear anal., 52, 1947-1959, (2003) · Zbl 1055.47047
[10] Sintamarian, A., Some pairs of multi-valued operators, Carpathian J. math., 21, 115-125, (2005) · Zbl 1101.47032
[11] Sintunavart, W.; Kumam, P., Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition, Appl. math. lett., 22, 1877-1881, (2009) · Zbl 1225.54028
[12] Sintunavart, W.; Kumam, P., Coincidence and common fixed points for generalized contraction multi-valued mappings, J. comput. anal. appl., 13, 2, 362-367, (2011) · Zbl 1221.47095
[13] Sintunavart, W.; Kumam, P., Gregus-type common fixed point theorems for tangential multivalued mappings of integral type in metric spaces, Int. J. math. math. sci., 2011, (2011), Article ID 923458, 12 pages · Zbl 1215.54026
[14] Suwannawit, J.; Petrot, N., Common fixed point theorem for hybrid generalized multivalued, Thai J. math., 9, 411-421, (2011)
[15] Kamran, T., Multivalued \(f\)-weakly Picard mappings, Nonlinear anal., 67, 2289-2296, (2007) · Zbl 1128.54024
[16] Sintunavart, W.; Kumam, P., Weak condition for generalized multi-valued \((f, \alpha, \beta)\)-weak contraction mappings, Appl. math. lett., 24, 460-465, (2011) · Zbl 1206.54064
[17] Berinde, V., Generalized contractions and applications, vol. 22, (1997), Cub Press Baia Mare, (in Romanian)
[18] Berinde, V., Iterative approximation of fixed points, (2002), Editura Efemeride Baia Mare · Zbl 1036.47037
[19] Berinde, V., On approximation of fixed points of weak \(\phi\)-contractive operators, Fixed point theory, 4, 131-142, (2003)
[20] Chatterjea, S.K., Fixed point theorems, C. R. acad. bulgare sci., 25, 727-730, (1972) · Zbl 0274.54033
[21] Ciric, Lj.B., Fixed point theory, () · Zbl 1122.47044
[22] Dugundji, J.; Granas, A., Weakly contractive maps and elementary domain invariance theorem, Bull. Greek math. soc., 19, 141-151, (1978) · Zbl 0417.54010
[23] Reich, S., Kannans fixed point theorem, Boll. unione mat. ital., 4, 1-11, (1971)
[24] Reich, S., Fixed points of contractive functions, Boll. unione mat. ital., 5, 26-42, (1972) · Zbl 0249.54026
[25] Rus, I.A., Generalized contractions and applications, (2001), Cluj University Press Cluj-Napoca · Zbl 0968.54029
[26] Zamfirescu, T., Fixed point theorems in metric spaces, Arch. math. (basel), 23, 292-298, (1972) · Zbl 0239.54030
[27] Reich, S., Some problems and results in fixed point theory, Contemp. math., 21, 179-187, (1983) · Zbl 0531.47048
[28] Kamran, T., Fixed points of asymptotically regular noncompatible maps, Demonstratio math., XXXVIII, 485-494, (2005) · Zbl 1070.54020
[29] Pathak, H.K.; Khan, M.S., Fixed and coincidence points of hybrid mappings, Arch. math. (Brno), 38, 201-208, (2002) · Zbl 1068.47073
[30] Kamran, T., Coincidence and fixed points for hybrid strict contractions, J. math. anal. appl., 299, 235-241, (2004) · Zbl 1064.54055
[31] Berinde, M.; Berinde, V., On general class of multivalued weakly Picard mappings, J. math. anal. appl., 326, 772-782, (2007) · Zbl 1117.47039
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.