Document Type : Research Paper
Authors
1 Chengdu University of Information Technology, Chengdu, China.
2 Department of Applied Mathematics, Chengdu University of Information Technology, China.
Abstract
Compared with [1], in this paper, We will give first some sufficient conditions under which a (c)-mapping possesses an Approximate Fixed Point Sequence (AFPS). And then, we will prove that (c)-mapping has a fixed point. Finally, we will check some special properties of the fixed point sets of these mappings, such as closedness, convexity.
Keywords
Main Subjects
- Som, S., Petruşel, A., Garai, H., & Dey, L. K. (2019). Some characterizations of Reich and Chatterjea type nonexpansive mappings. Journal of fixed point theory and applications, 21(4), 1-21. https://doi.org/10.1007/s11784-019-0731-x
- Browder, F. E. (1965). Nonexpansive nonlinear operators in a Banach space. Proceedings of the national academy of sciences of the United States of America, 54(4), 1041. DOI: 1073/pnas.54.4.1041
- Goebel, K., & Kirk, W. A. (1972). A fixed point theorem for asymptotically nonexpansive mappings. Proceedings of the American mathematical society, 35(1), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3
- Tomizawa, Y. (2017). Asymptotically quasi-nonexpansive mappings with respect to the Bregman distance in the intermediate sense. Fixed point theory, 18, 391-406.
- Luo, L., Ullah, R., Rahmat, G., Butt, S. I., & Numan, M. (2021). Approximating common fixed points of an evolution family on a metric space via Mann iteration. Journal of mathematics, 2021. https://doi.org/10.1155/2021/6764280
- Dong, Y. (2021). New inertial factors of the Krasnosel’skiĭ-Mann iteration. Set-valued and variational analysis, 29(1), 145-161. http://www.optimization-online.org/DB_FILE/2019/05/7191.pdf
- Lieder, F. (2021). On the convergence rate of the Halpern-iteration. Optimization letters, 15(2), 405-418. https://doi.org/10.1007/s11590-020-01617-9
- Ghiura, A. (2021). Convergence of modified Picard-Mann hybrid iteration process for nearly nonexpansive mappings. International journal of mathematics trends and technology (IJMTT), 6(12), 37-43. DOI:14445/22315373/IJMTT-V66I12P506
- Edalatpanah, S. A. (2019). A nonlinear approach for neutrosophic linear programming. Journal of applied research on industrial engineering, 6(4), 367-373. (In Persian). DOI: 22105/jarie.2020.217904.1137
- Atailia, S., Redjel, N., & Dehici, A. (2020). Some fixed point results for (c)-mappings in Banach spaces. Journal of fixed point theory and applications, 22, 1-14. https://doi.org/10.1007/s11784-020-00787-4
- Weng, S. Q. (2019). Some fixed point results involving a general LW-type cyclic mapping in complete b-metric-like spaces. International journal of research in industrial engineering, 8(3), 262-273. (In Persian). DOI: 22105/riej.2019.195844.1093
- Bae, J. S. (1984). Fixed point theorems of generalized nonexpansive maps. Journal of the Korean mathematical society, 21(2), 233-248.
- Smyth, M. A. (1997). The fixed point problem for generalised nonexpansive maps. Bulletin of the Australian mathematical society, 55(1), 45-61. https://doi.org/10.1017/S0004972700030525
- Browder, F. E., & Petryshyn, W. (1966). The solution by iteration of nonlinear functional equations in Banach spaces. Bulletin of the American mathematical society, 72(3), 571-575.
- Weng, S., Zhang, Y., & Wu, D. P. (2018). Fixed point theorems of LW-type Lipschitz cyclic mappings in complete B-metric-like spaces. International journal of research in industrial engineering, 7(2), 136-146. (In Persian). https://dx.doi.org/10.22105/riej.2018.143285.1051
- Goebel, K., & Kirk, W. A. (1983). Iteration processes for nonexpansive mappings. Math, 21, 115-123.