Common fixed points for commuting and compatible maps

Ismat Beg; Akbar Azam

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

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

Abstract

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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.

How to cite

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Ismat 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

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  1. [1] J.P. Aubin, Applied Abstract Analysis, John Wiley and Sons, New York 1977. 
  2. [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. [3] I. Beg and A. Azam, Fixed points of multivalued locally contractive mappings, Boll. U.M.I. 4-A (7) (1990), 227-233. 
  4. [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. [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. [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. [7] O. Hadzic, Common fixed point theorems for family of mappings in complete metric spaces, Math. Japonica 29 (1984), 127-134. Zbl0537.54040
  8. [8] T. Hu, Fixed points theorems for multivalued mappings, Canad. Math. Bull. 23 (1980), 193-197. Zbl0436.54037
  9. [9] K. Iseki, Multivalued contraction mappings in complete metric spaces, Rend. Sem. Math. Univ. Padova 53 (1975), 15-19. Zbl0328.54030
  10. [10] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261-263. Zbl0321.54025
  11. [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. [12] H. Kaneko, Single valued and multivalued f-contractions, Boll. U.M.I. 4A (1985), 29-33. Zbl0568.54031
  13. [13] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 2 (1969), 526-529. Zbl0194.44904
  14. [14] S.B. Nadler, Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-488. Zbl0187.45002
  15. [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. [16] B.K. Ray, On Ciric's fixed point theorem, Fund. Math. 94 (1977), 221-229. Zbl0345.54044
  17. [17] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121-124. Zbl0211.26002
  18. [18] B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290. Zbl0365.54023
  19. [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. [20] C.S. Wong, Common fixed points of two mappings, Pacific J. Math. 49 (1) (1973), 299-312. Zbl0269.54028

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