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

  1. 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 applications21(4), 1-21. https://doi.org/10.1007/s11784-019-0731-x
  2. Browder, F. E. (1965). Nonexpansive nonlinear operators in a Banach space. Proceedings of the national academy of sciences of the United States of America54(4), 1041. DOI: 1073/pnas.54.4.1041
  3. Goebel, K., & Kirk, W. A. (1972). A fixed point theorem for asymptotically nonexpansive mappings. Proceedings of the American mathematical society35(1), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3
  4. Tomizawa, Y. (2017). Asymptotically quasi-nonexpansive mappings with respect to the Bregman distance in the intermediate sense. Fixed point theory18, 391-406.
  5. 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 mathematics2021. https://doi.org/10.1155/2021/6764280
  6. Dong, Y. (2021). New inertial factors of the Krasnosel’skiĭ-Mann iteration. Set-valued and variational analysis29(1), 145-161. http://www.optimization-online.org/DB_FILE/2019/05/7191.pdf
  7. Lieder, F. (2021). On the convergence rate of the Halpern-iteration. Optimization letters15(2), 405-418. https://doi.org/10.1007/s11590-020-01617-9
  8. 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
  9. Edalatpanah, S. A. (2019). A nonlinear approach for neutrosophic linear programming. Journal of applied research on industrial engineering6(4), 367-373. (In Persian). DOI: 22105/jarie.2020.217904.1137
  10. Atailia, S., Redjel, N., & Dehici, A. (2020). Some fixed point results for (c)-mappings in Banach spaces. Journal of fixed point theory and applications22, 1-14. https://doi.org/10.1007/s11784-020-00787-4
  11. 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 engineering8(3), 262-273. (In Persian). DOI: 22105/riej.2019.195844.1093
  12. Bae, J. S. (1984). Fixed point theorems of generalized nonexpansive maps. Journal of the Korean mathematical society21(2), 233-248.
  13. Smyth, M. A. (1997). The fixed point problem for generalised nonexpansive maps. Bulletin of the Australian mathematical society55(1), 45-61. https://doi.org/10.1017/S0004972700030525
  14. Browder, F. E., & Petryshyn, W. (1966). The solution by iteration of nonlinear functional equations in Banach spaces. Bulletin of the American mathematical society72(3), 571-575.
  15. 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 engineering7(2), 136-146. (In Persian). https://dx.doi.org/10.22105/riej.2018.143285.1051
  16. Goebel, K., & Kirk, W. A. (1983). Iteration processes for nonexpansive mappings.  Math21, 115-123.