# Common fixed points for commuting and compatible maps

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1996)

- Volume: 16, Issue: 2, page 121-135
- ISSN: 1509-9407

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topIsmat Beg, and Akbar Azam. "Common fixed points for commuting and compatible maps." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 16.2 (1996): 121-135. <http://eudml.org/doc/275912>.

@article{IsmatBeg1996,

abstract = {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.},

author = {Ismat Beg, Akbar Azam},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {fixed point; multivalued mapping; Meir-Keeler type mapping; fixed point theorems; multivalued hybrid contractions; Meir-Keeler type multivalued maps; metric space},

language = {eng},

number = {2},

pages = {121-135},

title = {Common fixed points for commuting and compatible maps},

url = {http://eudml.org/doc/275912},

volume = {16},

year = {1996},

}

TY - JOUR

AU - Ismat Beg

AU - Akbar Azam

TI - Common fixed points for commuting and compatible maps

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 1996

VL - 16

IS - 2

SP - 121

EP - 135

AB - 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.

LA - eng

KW - fixed point; multivalued mapping; Meir-Keeler type mapping; fixed point theorems; multivalued hybrid contractions; Meir-Keeler type multivalued maps; metric space

UR - http://eudml.org/doc/275912

ER -

## References

top- [1] J.P. Aubin, Applied Abstract Analysis, John Wiley and Sons, New York 1977.
- [2] J.P. Aubin and J. Siegel, Fixed points and stationary points of dissipative multivalued maps, Proc. Amer. Math. Soc. 78 (1980), 391-398. Zbl0446.47049
- [3] I. Beg and A. Azam, Fixed points of multivalued locally contractive mappings, Boll. U.M.I. 4-A (7) (1990), 227-233.
- [4] I. Beg and A. Azam, Fixed points of asymptotically regular multivalued mappings, J. Austral. Math. Soc. (Series A) 53 (3) (1992), 313-326.
- [5] L.S. Dube, A theorem on common fixed points of multivalued mappings, Annal. Soc. Sci. Bruxells 84 (4) (1975), 463-468. Zbl0309.54036
- [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.
- [7] O. Hadzic, Common fixed point theorems for family of mappings in complete metric spaces, Math. Japonica 29 (1984), 127-134. Zbl0537.54040
- [8] T. Hu, Fixed points theorems for multivalued mappings, Canad. Math. Bull. 23 (1980), 193-197. Zbl0436.54037
- [9] K. Iseki, Multivalued contraction mappings in complete metric spaces, Rend. Sem. Math. Univ. Padova 53 (1975), 15-19. Zbl0328.54030
- [10] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261-263. Zbl0321.54025
- [11] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (3) (1988), 977-983. Zbl0661.54043
- [12] H. Kaneko, Single valued and multivalued f-contractions, Boll. U.M.I. 4A (1985), 29-33. Zbl0568.54031
- [13] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 2 (1969), 526-529. Zbl0194.44904
- [14] S.B. Nadler, Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-488. Zbl0187.45002
- [15] S. Park and J.S. Bae, Extensions of a fixed point theorem of Meir and Keeler, Ark. Math. 19 (1981), 223-228. Zbl0483.47040
- [16] B.K. Ray, On Ciric's fixed point theorem, Fund. Math. 94 (1977), 221-229. Zbl0345.54044
- [17] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121-124. Zbl0211.26002
- [18] B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290. Zbl0365.54023
- [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. Zbl0711.54028
- [20] C.S. Wong, Common fixed points of two mappings, Pacific J. Math. 49 (1) (1973), 299-312. Zbl0269.54028