Convergence of agarwal-type iteration process to common fixed points of two generalized -nonexpansive mappings in uniformly convex Banach spaces
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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.
Article Details
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Keywords
Generalized -nonexpansive mapping, Agarwal iteration process, common fixed point
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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