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Some results on coincidence points

  • Abdul Latif (a1) and Ian Tweddle (a2)
Abstract

In this paper we prove some coincidence point theorems for nonself single-valued and multivalued maps satisfying a nonexpansive condition. These extend fixed point theorems for multivalued maps of a number of authors.

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[1]N.A. Assad and W.A. Kirk , ‘Fixed point theorems for set-valued mappings of contractive type’, Pacific J. Math. 43 (1972), 553562.

[6]S. Itoh and W. Takahashi , ‘Single-valued mappings, multivalued mappings and fixed point theorems’, J. Math. Anal. Appl. 59 (1977), 514521.

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[9]E. Lami Dozo , ‘Multivalued nonexpansive mappings and Opial's condition’, Proc. Amer. Math. Soc. 38 (1973), 286292.

[11]T.C. Lim , ‘A fixed point theorem for multivalued nonexpansive mapping in a uniformly convex Banach space’, Bull. Amer. Math. Soc. 80 (1974), 11231126.

[12]J.T. Markin , ‘A fixed point theorem for set-valued mappings’, Bull. Amer. Math. Soc. 74 (1968), 639640.

[14]C. Martinez-Yanez , ‘A remark on weakly inward contractions’, Nonlinear Anal. 16 (1991), 847848.

[15]S.B. Nadler , ‘Multivalued contraction mappings’, Pacific J. Math. 30 (1969), 475488.

[16]Z. Opial , ‘Weak convergence of the sequence of successive approximations for nonexpansive mappings’, Bull. Amer. Math. Soc. 73 (1967), 591597.

[18]S. Reich , ‘Approximate selection, best approximation, fixed points and invariant sets’, J. Math. Anal. Appl. 62 (1978), 104113.

[19]R.E. Smithson , ‘Fixed points for contractive multifunctions’, Proc. Amer. Math. Soc. 27 (1971), 192194.

[20]K. Yanagi , ‘On some fixed point theorems for multivalued mappings’, Pacific J. Math. 87 (1980), 233240.

[21]H-W. Yi and Y-C. Zhao , ‘Fixed point theorems for weakly inward multivalued mappings and their randomizations’, J. Math. Anal. Appl. 183 (1994), 613619.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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