Approximate fixed points for nonexpansive mappings in uniformly convex spaces
W. A. Kirk, Carlos Martinez-Yanez (1990)
Annales Polonici Mathematici
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W. A. Kirk, Carlos Martinez-Yanez (1990)
Annales Polonici Mathematici
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S. Naimpally, K. Singh, J. Whitfield (1984)
Fundamenta Mathematicae
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Somashekhar Naimpally, Kanhaya Lal Singh, J. H. M. Whitfield (1983)
Commentationes Mathematicae Universitatis Carolinae
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W. Kirk, W. Ray (1979)
Studia Mathematica
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Espínola, Rafa, Hussain, Nawab (2010)
Fixed Point Theory and Applications [electronic only]
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K. Goebel (1970)
Compositio Mathematica
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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...
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...
Ghosh, M.K., Debnath, L. (1997)
International Journal of Mathematics and Mathematical Sciences
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T. D. Narang (2014)
Annales UMCS, Mathematica
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A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject