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Fixed point theorems for set nd single valued maps witout continuity and compatibility

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The new concept of weak commutativity of type (KB) is used to prove some fixed point theorems for set and single-valued mappings. We show that continuity of any mapping is not necessary for the existence of common fixed point. We also show that completeness of the whole space can be replaced by a weaker condition.
Wydawca
Rocznik
Strony
649--658
Opis fizyczny
Bibliogr. 17 poz.
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autor
autor
Bibliografia
  • [1] T. H. Chang, Fixed point theorems of contractive type set valued mappings, Math. Japonica 38 No. 4 (1993), 675-690.
  • [2] B. Fisher, Common fixed points of mappings and set valued mappings on a metric space, Kyungpook Math. J. 25 (1985), 35-42.
  • [3] B. Fisher and S. Sessa, Two common fixed point theorems for weakly commuting mappings, Periodica Math. Hungarica 20(3) (1989), 207-218.
  • [4] G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), 771-779.
  • [5] G. Jungck and B. E. Rhoades, Some fixed point theorems for compatible maps, Internat. J. Math. & Math. Sci. 16(3) (1993), 417-428.
  • [6] G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 16(3) (1998), 227-228.
  • [7] I. Kubiaczyk and B. Deshpande, Noncompatibility, discontinuity in consideration of common fixed point of set and single-valued maps, Southeast Asian Bull. of Math. accepted for publication.
  • [8] S. Krzyśka and I. Kubiaczyk, Fixed point theorems for upper semicontinuous and weakly- weakly upper semicontinuous multivalued mappings, Math. Japonica 47(2) (1998), 237-240.
  • [9] R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), 436-440.
  • [10] R. P. Pant, Common fixed point theorems for contractive maps, J. Math. Anal. Appl. 226 (1998), 251-258.
  • [11] R. P. Pant, Common fixed points of Lipschitz type mappings pair, J. Math. Anal. Appl. 240 (1999), 280-283.
  • [12] R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1999), 284-289.
  • [13] H. K. Pathak, Y. J. Cho and Kang, Remarks on R-weakly commuting mappings and common fixed point theorems, Bull. Korean Math. Soc. 34 (1997), 247-257.
  • [14] R. A. Rashwan and M. A. Ahmed, Common fixed points for weakly compatible mappings, Italian J. Pure and Appl. Math. (8) (2000), 35-44.
  • [15] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) 32(46) (1982), 149-153.
  • [16] S. Sessa amd M. S. Khan, Some remarks in best approximation theory, Math. J. Toyoma Univ. 17 (1994), 151-165.
  • [17] K. Tas, M. Telki and B. Fisher, Common fixed point theorems for compatible mappings, Internat J. Math. and Math. Sci. 19(3) (1996), 451-456.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0035-0014
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