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Date Published:
30/04/2019
Online Published:
30/04/2019
Abstract Views: 197
Views PDF: 61
Views PDF: 61
Section
Natural Sciences Issue (Vietnamese)
How to Cite
Nguyen, K. N., & Nguyen, T. H. (2019). Convergence of agarwal-type iteration process to common fixed points of two generalized -nonexpansive mappings in uniformly convex Banach spaces. Dong Thap University Journal of Science, 37, 70-77. https://doi.org/10.52714/dthu.37.4.2019.685
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Convergence of agarwal-type iteration process to common fixed points of two generalized -nonexpansive mappings in uniformly convex Banach spaces
Main Article Content
Abstract
In this paper, we come up with establishing the weak and strong convergence of Agarwal type iteration process to common fixed points of two generalized -nonexpansive mappings in uniformly convex Banach spaces. These results are the extensions of the main ones found in [6] and [9]. In addition, some examples are provided for illustration.
Keywords
Generalized -nonexpansive mapping, Agarwal iteration process, common fixed point
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
[1]. K. Aoyama and F. Kohsaka (2011), “Fixed point theorem for a-nonexpansive mapping in Banach space”, Nonlinear Anal., (74), pp. 4387-4391. [2]. B. Beauzamy (1982), Introduction to Banach spaces and their geometry, North-Holland Mathematics Studies, vol.68, North-Holland, Amsterdam.
[3]. F. E. Browder (1965), “Nonexpansive nonlinear operators in a Banach space”, Proc. Nat. Acad. Sci. USA, (54), pp. 1041-1044.
[4]. E. L. Dozo (1973), “Multivalued nonexpansive mappings and Opial's condition”, Proc. Amer. Math. Soc., 38(2), pp. 286-292.
[5] K. Goebel and W. A. Kirk (1990), Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics, vol.28. Cambridge University Press, Cambridge.
[6]. R. Pant and R. Shukla (2017), “Approximating fixed points of generalized a-nonexpansive mappings in Banach spaces”, Numer. Funct. Anal. Optim., 38 (2), pp. 248-266.
[7]. H. Piri, B.Daraby, S. Rahrovi and M. Ghasemi (2018), “Approximating fixed points of generalized a-nonexpansive mappings in Banach spaces by new faster iteration process”, Numer. Algorithms, pp. 1-20, first online.
[8]. J. Schu (1991), “Weak and strong convergence to fixed points of asymptotically nonexpansive mappings”, Bull. Aust. Math. Soc., 43 (1), pp. 153-159.
[9]. N. Shahzad and R. Al-Dubiban (2006), “Approximating common fixed points of nonexpansive mappings in Banach spaces”, Georgian Math. J., 13 (3), pp. 529-537.
[10]. T. Suzuki (2011), “Fixed point theorems and convergence theorems for some generalized nonexpansive mappings”, J. Math. Anal. Appl., (340), pp. 1088-1095.
[3]. F. E. Browder (1965), “Nonexpansive nonlinear operators in a Banach space”, Proc. Nat. Acad. Sci. USA, (54), pp. 1041-1044.
[4]. E. L. Dozo (1973), “Multivalued nonexpansive mappings and Opial's condition”, Proc. Amer. Math. Soc., 38(2), pp. 286-292.
[5] K. Goebel and W. A. Kirk (1990), Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics, vol.28. Cambridge University Press, Cambridge.
[6]. R. Pant and R. Shukla (2017), “Approximating fixed points of generalized a-nonexpansive mappings in Banach spaces”, Numer. Funct. Anal. Optim., 38 (2), pp. 248-266.
[7]. H. Piri, B.Daraby, S. Rahrovi and M. Ghasemi (2018), “Approximating fixed points of generalized a-nonexpansive mappings in Banach spaces by new faster iteration process”, Numer. Algorithms, pp. 1-20, first online.
[8]. J. Schu (1991), “Weak and strong convergence to fixed points of asymptotically nonexpansive mappings”, Bull. Aust. Math. Soc., 43 (1), pp. 153-159.
[9]. N. Shahzad and R. Al-Dubiban (2006), “Approximating common fixed points of nonexpansive mappings in Banach spaces”, Georgian Math. J., 13 (3), pp. 529-537.
[10]. T. Suzuki (2011), “Fixed point theorems and convergence theorems for some generalized nonexpansive mappings”, J. Math. Anal. Appl., (340), pp. 1088-1095.
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