- Volume 47 Issue 3
We prove a common fixed point theorem for S-contraction mappings without continuity. Using this result we obtain an approximating curve for S-nonexpansive mappings in a Banach space and prove Browder's type strong convergence theorem for this approximating curve. The demiclosedness principle for S-nonexpansive mappings is also established.
demicontinuity;R-weakly commutativity;S-contraction mapping;S-nonexpansive mapping
- M. A. Al-Thagafi, Common fixed points and best approximation, J. Approx. Theory 85 (1996), no. 3, 318-323. https://doi.org/10.1006/jath.1996.0045
- F. E. Browder, Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces, Arch. Rational Mech. Anal. 24 (1967), 82-90.
- W. G. Dotson, Jr., Fixed point theorems for non-expansive mappings on star-shaped subsets of Banach spaces, J. London Math. Soc. (2) 4 (1972), 408-410. https://doi.org/10.1112/jlms/s2-4.3.408
- G. Jungck, Coincidence and fixed points for compatible and relatively nonexpansive maps, Internat. J. Math. Math. Sci. 16 (1993), no. 1, 95-100. https://doi.org/10.1155/S0161171293000110
- Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. https://doi.org/10.1090/S0002-9904-1967-11761-0
- R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), no. 2, 436-440. https://doi.org/10.1006/jmaa.1994.1437
- S. Park, On f-nonexpansive maps, J. Korean Math. Soc. 16 (1979), no. 1, 29-38.
- N. Shahzad, Invariant approximations and R-subweakly commuting maps, J. Math. Anal. Appl. 257 (2001), no. 1, 39-45. https://doi.org/10.1006/jmaa.2000.7274
- Some Existence and Convergence Theorems for Nonexpansive Type Mappings vol.2013, 2013, https://doi.org/10.1155/2013/539723