Common fixed points for commuting and compatible maps on compacta
HTML articles powered by AMS MathViewer
- by Gerald Jungck PDF
- Proc. Amer. Math. Soc. 103 (1988), 977-983 Request permission
Abstract:
Compatible maps—a generalization of commuting maps—are characterized in terms of coincidence points, and common fixed point theorems for compatible maps and commuting maps on compact metric spaces are obtained.References
- Chêng Chun Chang, On a fixed point theorem of contractive type, Comment. Math. Univ. St. Paul. 32 (1983), no. 1, 15–19. MR 701928
- Shih Sen Chang, A common fixed point theorem for commuting mappings, Proc. Amer. Math. Soc. 83 (1981), no. 3, 645–652. MR 627712, DOI 10.1090/S0002-9939-1981-0627712-7
- C. E. Chidume, Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings, Proc. Amer. Math. Soc. 99 (1987), no. 2, 283–288. MR 870786, DOI 10.1090/S0002-9939-1987-0870786-4
- G. Das and J. P. Debata, A note on fixed points of commuting mappings of contractive type, Indian J. Math. 27 (1985), no. 1-3, 49–51 (1986). MR 852133 K. M. Das and V. Naik, Common fixed point theorems for commuting maps on metric spaces, Proc. Amer. Math. Soc. 77 (1979), 269-373.
- Brian Fisher, A common fixed point theorem for four mappings on a compact metric space, Bull. Inst. Math. Acad. Sinica 12 (1984), no. 3, 249–252. MR 764955
- Brian Fisher, Common fixed points of four mappings, Bull. Inst. Math. Acad. Sinica 11 (1983), no. 1, 103–113. MR 718906
- M. S. Khan and Brian Fisher, Some fixed point theorems for commuting mappings, Math. Nachr. 106 (1982), 323–326. MR 675765, DOI 10.1002/mana.19821060127
- Gerald Jungck, Periodic and fixed points, and commuting mappings, Proc. Amer. Math. Soc. 76 (1979), no. 2, 333–338. MR 537100, DOI 10.1090/S0002-9939-1979-0537100-0
- Gerald Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), no. 4, 261–263. MR 400196, DOI 10.2307/2318216
- Gerald Jungck, A common fixed point theorem for commuting maps on $L$-spaces, Math. Japon. 25 (1980), no. 1, 81–85. MR 571267 —, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), 771-779. —, Compatible mappings and common fixed points (2), Internat. J. Math. Math. Sci. 9 (1986), 285-288.
- Solomon Leader, Uniformly contractive fixed points in compact metric spaces, Proc. Amer. Math. Soc. 86 (1982), no. 1, 153–158. MR 663887, DOI 10.1090/S0002-9939-1982-0663887-2
- R. P. Pant, Common fixed points of two pairs of commuting mappings, Indian J. Pure Appl. Math. 17 (1986), no. 2, 187–192. MR 830556
- Sehie Park and Jong Sook Bae, Extensions of a fixed point theorem of Meir and Keeler, Ark. Mat. 19 (1981), no. 2, 223–228. MR 650495, DOI 10.1007/BF02384479
- Barada K. Ray, Remarks on a fixed-point theorem of Gerald Jungck, J. Univ. Kuwait Sci. 12 (1985), no. 2, 169–172 (English, with Arabic summary). MR 827180
- Salvatore Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32(46) (1982), 149–153. MR 710984
- Salvatore Sessa and Brian Fisher, On fixed points of weakly commuting mappings in compact metric spaces, Jñānābha 15 (1985), 79–91. MR 822927
- S. L. Singh and S. P. Singh, A fixed point theorem, Indian J. Pure Appl. Math. 11 (1980), no. 12, 1584–1586. MR 617835
- B. M. L. Tivari and S. L. Singh, A note on recent generalizations of Jungck contraction principle, J. Uttar Pradesh Gov. Colleges Acad. Soc. 3 (1986), no. 1, 13–18 (English, with Hindi summary). MR 914072
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 977-983
- MSC: Primary 54H25; Secondary 54E45
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947693-2
- MathSciNet review: 947693