Approximating fixed points of nonexpansive and generalized nonexpansive mappings.
Maiti, M., Saha, B. (1993)
International Journal of Mathematics and Mathematical Sciences
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Maiti, M., Saha, B. (1993)
International Journal of Mathematics and Mathematical Sciences
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Ghosh, M.K., Debnath, L. (1997)
International Journal of Mathematics and Mathematical Sciences
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Kittipong Sitthikul, Satit Saejung (2009)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, weak and strong convergence of finite step iteration sequences to a common fixed point for a pair of a finite family of nonexpansive mappings and a finite family of asymptotically nonexpansive mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented.
Kaewcharoen, A., Kirk, W.A. (2006)
Fixed Point Theory and Applications [electronic only]
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A. Anthony Eldred, W. A. Kirk, P. Veeramani (2005)
Studia Mathematica
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The notion of proximal normal structure is introduced and used to study mappings that are "relatively nonexpansive" in the sense that they are defined on the union of two subsets A and B of a Banach space X and satisfy ∥ Tx-Ty∥ ≤ ∥ x-y∥ for all x ∈ A, y ∈ B. It is shown that if A and B are weakly compact and convex, and if the pair (A,B) has proximal normal structure, then a relatively nonexpansive mapping T: A ∪ B → A ∪ B satisfying (i) T(A) ⊆ B and T(B) ⊆ A, has a proximal point in...
K. Goebel, T. Kuczumow (1979)
Colloquium Mathematicae
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Rhoades, B.E., Temir, Seyit (2006)
International Journal of Mathematics and Mathematical Sciences
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Xiaolong Qin, Yongfu Su, Meijuan Shang (2007)
Open Mathematics
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Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T 1, T 2 and T 3: K → E be asymptotically nonexpansive mappings with k n, l n and j n. [1, ∞) such that Σn=1∞(k n − 1) < ∞, Σn=1∞(l n − 1) < ∞ and Σn=1∞(j n − 1) < ∞, respectively and F nonempty, where F = x ∈ K: T 1x = T 2x = T 3 x = xdenotes the common fixed points set of T 1, T 2 and T 3. Let α n, α′ n and α″ n be real sequences in (0, 1) and ∈ ≤ α...
Liu, Guimei, Lei, Deng, Li, Shenghong (2000)
International Journal of Mathematics and Mathematical Sciences
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Zeqing Liu, Ravi P. Agarwal, Chi Feng, Shin Min Kang (2005)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results...