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Search Results: 1 - 10 of 3961 matches for " Suzuki Tomonari "
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Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces
Tomonari Suzuki
Abstract and Applied Analysis , 2006, DOI: 10.1155/aaa/2006/58684
Abstract: One of our main results is the following convergencetheorem for one-parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E, and let {T(t):t∈ℝ
An example for a one-parameter nonexpansive semigroup
Tomonari Suzuki
Abstract and Applied Analysis , 2005, DOI: 10.1155/aaa.2005.173
Abstract: We give one example for a one-parameter nonexpansive semigroup.This example shows that there exists a one-parameter nonexpansivesemigroup {T(t):t≥0} on a closed convex subset C of a Banach space E such that limt→∞‖(1/t)∫0tT(s)xds−x‖=0for some x∈C, which is not a common fixed point of {T(t):t≥0}.
Characterizations of fixed points of nonexpansive mappings
Tomonari Suzuki
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.1723
Abstract: Using the notion of Banach limits, we discuss the characterization of fixed points of nonexpansive mappings in Banach spaces. Indeed, we prove that the two sets of fixed points of a nonexpansive mapping and some mapping generated by a Banach limit coincide. In our discussion, we may not assume the strict convexity of the Banach space.
Meir-Keeler Contractions of Integral Type Are Still Meir-Keeler Contractions
Tomonari Suzuki
International Journal of Mathematics and Mathematical Sciences , 2007, DOI: 10.1155/2007/39281
Abstract: We prove that the recent fixed point theorem for contractions of integral type due to Branciari is a corollary of the famous Meir-Keeler fixed point theorem. We also prove that Meir-Keeler contractions of integral type are still Meir-Keeler contractions.
Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces
Tomonari Suzuki
Abstract and Applied Analysis , 2006,
Abstract: One of our main results is the following convergence theorem for one-parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E , and let { T( t ):t∈ + } be a strongly continuous semigroup of nonexpansive mappings on C . Fix u∈C and t 1 , t 2 ∈ + with t 1 < t 2 . Define a sequence { x n } in C by x n = ( 1 α n ) / ( t 2 t 1 ) ∫ t 1 t 2 T( s ) x n ds+ α n u for n∈ , where { α n } is a sequence in ( 0,1 ) converging to 0 . Then { x n } converges strongly to a common fixed point of { T( t ):t∈ + } .
Fixed point theorems for asymptotically contractive mappings
Tomonari Suzuki
Le Matematiche , 2003,
Abstract: In this short paper, we prove fixed point theorems for nonexpansive mappings whose domains are unbounded subsets of Banach spaces. These theorems are generalizations of Penot's result in [4].
Several fixed point theorems concerning -distance
Suzuki Tomonari
Fixed Point Theory and Applications , 2004,
Abstract: Using the notion of -distance, we prove several fixed point theorems, which are generalizations of fixed point theorems by Kannan, Meir-Keeler, Edelstein, and Nadler. We also discuss the properties of -distance.
Convergence of the Sequence of Successive Approximations to a Fixed Point
Tomonari Suzuki
Fixed Point Theory and Applications , 2010, DOI: 10.1155/2010/716971
Abstract: If (X,d) is a complete metric space and T is a contraction on X, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations {Tnx} of T starting from any point x∈X converges to a unique fixed point. In this paper, using the concept of τ-distance, we obtain simple, sufficient, and necessary conditions of the above conclusion.
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces
Suzuki Tomonari
Fixed Point Theory and Applications , 2006,
Abstract: We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
Several fixed point theorems concerning -distance
Tomonari Suzuki
Fixed Point Theory and Applications , 2004, DOI: 10.1155/s168718200431003x
Abstract: Using the notion of -distance, we prove several fixed point theorems, which are generalizations of fixed point theorems by Kannan, Meir-Keeler, Edelstein, and Nadler. We also discuss the properties of -distance.
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