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Fixed points of asymptotically regular multivalued mappings

  • Ismat Beg (a1) and Akbar Azam (a2)
Abstract
Abstract

Some results on fixed point of asymptotically regular multivalued mapping are obtained in metric spaces. The structure of common fixed points and coincidence points of a pair of compatible multivalued mappings is also discussed. Our work generalizes known results of Aubin and Siegel, Dube, Dube and Singh, Hardy and Rogers, Hu, Iseki, Jungck, Kaneko, Nadler, Ray and Shiau, Tan and Wong.

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[3] J. P. Aubin and J. Siegel , ‘Fixed points and stationary points of dissipative multivalued maps’, Proc. Amer. Math. Soc. 78 (1980), 391398.

[7] H. W. Engl , ‘Weak convergence of asymptotically regular sequences for nonexpansive mappings and connections with certain Chebyshef-centers’, Nonlinear Anal. 1 (5) (1977), 495501.

[9] G. E. Hardy and T. D. Rogers , ‘A generalization of a fixed point theorem of Reich’, Canad. Math. Bull. 16 (1973), 201206.

[10] T. Hu , ‘Fixed point theorems for multivalued mappings’, Canad. Math. Bull. 23 (1980), 193197.

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

[13] G. Jungck , ‘Commuting mappings and fixed points’, Amer. Math. Monthly 83 (1976), 261263.

[14] G. Jungck , ‘Compatible mappings and common fixed points’, Internat. J. Math. and Math. Sci. 9 (1986), 771779.

[16] G. Jungck , ‘Common fixed points for commuting and compatible maps on compacta’, Proc. Amer. Math. Soc. 103 (3) (1988), 977983.

[18] R. Kannan , ‘Fixed point theorems in reflexive Banach space’, Proc. Amer. Math. Soc. 38 (1973), 111118.

[21] S. B. Nadler Jr, ‘Multivalued contraction mappings’, Pacific J. Math. 30 (1969), 475480.

[24] B. E. Rhoades , ‘A comparison of various definitions of contractive mappings’, Trans. Amer. Math. Soc. 226 (1977), 257290.

[25] B. E. Rhoades , ‘Contractive definitions revisited, Topological methods in nonlinear functional analysis’, Contemporary Math., Amer. Math. Soc. 21(1983), 189205.

[26] B. E. Rhoades , S. L. Singh and C. Kulshrestha , ‘Coincidence theorem for some multi- valued mappings’, Internat. J. Math. and Math. Sci. 7 (3) (1984), 429434.

[28] B. E. Rhoades , S. Park and K. B. Moon , ‘On generalization of the Meir-Keeler type contraction maps’, J. Math. Anal. Appl. 146 (1990), 482494.

[29] S. Sessa , B. E. Rhoades and M. S. Khan , ‘On common fixed points of compatible mappings in metric and Banach spaces’, Internat. J. Math. and Math. Sci. 11 (2) (1988), 375392.

[30] C. Shiau , K. K. Tan and C. S. Wong , ‘A class of quasi-nonexpansive multivalued maps’, Canad. Math. Bull. 18 (1975), 709714.

[31] C. S. Wong , ‘Common fixed points of two mappings’, Pacific J. Math. 48 (1973), 299312.

[32] C. S. Wong , ‘On Kannan maps’, Proc. Amer. Math. Soc. 47 (1975), 105111.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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