Fixed point theorems of multivalued hybrid contractions and Meir-Keeler type multivalued maps are obtained in a metric space. Our results generalize corresponding results of Aubin and Siegel, Dube, Dube and Singh, Hadzic, Iseki, Jungck, Kaneko, Nadler, Park and Bae, Reich, Ray and many others.
@article{bwmeta1.element.bwnjournal-article-div16i2n2bwm,
author = {Ismat Beg and Akbar Azam},
title = {Common fixed points for commuting and compatible maps},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {16},
year = {1996},
pages = {121-135},
zbl = {0912.47033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div16i2n2bwm}
}
Ismat Beg; Akbar Azam. Common fixed points for commuting and compatible maps. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996) pp. 121-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div16i2n2bwm/
[000] [1] J.P. Aubin, Applied Abstract Analysis, John Wiley and Sons, New York 1977.
[001] [2] J.P. Aubin and J. Siegel, Fixed points and stationary points of dissipative multivalued maps, Proc. Amer. Math. Soc. 78 (1980), 391-398. | Zbl 0446.47049
[002] [3] I. Beg and A. Azam, Fixed points of multivalued locally contractive mappings, Boll. U.M.I. 4-A (7) (1990), 227-233.
[003] [4] I. Beg and A. Azam, Fixed points of asymptotically regular multivalued mappings, J. Austral. Math. Soc. (Series A) 53 (3) (1992), 313-326.
[004] [5] L.S. Dube, A theorem on common fixed points of multivalued mappings, Annal. Soc. Sci. Bruxells 84 (4) (1975), 463-468. | Zbl 0309.54036
[005] [6] L.S. Dube and S.P. Singh, On multivalued contraction mappings, Bull. Math. de la Soc. Sci. Math. de la. R.S. de Roumanie 14 (62) (3) (1970), 307-310.
[006] [7] O. Hadzic, Common fixed point theorems for family of mappings in complete metric spaces, Math. Japonica 29 (1984), 127-134. | Zbl 0537.54040
[007] [8] T. Hu, Fixed points theorems for multivalued mappings, Canad. Math. Bull. 23 (1980), 193-197. | Zbl 0436.54037
[008] [9] K. Iseki, Multivalued contraction mappings in complete metric spaces, Rend. Sem. Math. Univ. Padova 53 (1975), 15-19. | Zbl 0328.54030
[009] [10] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261-263. | Zbl 0321.54025
[010] [11] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (3) (1988), 977-983. | Zbl 0661.54043
[011] [12] H. Kaneko, Single valued and multivalued f-contractions, Boll. U.M.I. 4A (1985), 29-33. | Zbl 0568.54031
[012] [13] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 2 (1969), 526-529. | Zbl 0194.44904
[013] [14] S.B. Nadler, Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-488. | Zbl 0187.45002
[014] [15] S. Park and J.S. Bae, Extensions of a fixed point theorem of Meir and Keeler, Ark. Math. 19 (1981), 223-228. | Zbl 0483.47040
[015] [16] B.K. Ray, On Ciric's fixed point theorem, Fund. Math. 94 (1977), 221-229. | Zbl 0345.54044
[016] [17] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121-124. | Zbl 0211.26002
[017] [18] B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290. | Zbl 0365.54023
[018] [19] B.E. Rhoades, S. Park and K.B. Moon, On generalization of Meir-Keeler type contraction maps, J. Math. Anal. Appl. 146 (1990), 482-494. | Zbl 0711.54028
[019] [20] C.S. Wong, Common fixed points of two mappings, Pacific J. Math. 49 (1) (1973), 299-312. | Zbl 0269.54028