finding fixed points of functions

... common fixed point of f and S Since gu = fz, following arguments similar to those given above we conclude that fz is a common fixed point of g and T as well Now we show the uniqueness of fixed ... common fixed point of f, g, S and T From (2.1), we obtain Abbas et al Fixed Point Theory and Applications 2011, 2011:41 http://www.fixedpointtheoryandapplications.com/content/2011/1/41 Page of 11 ... article as: Abbas et al.: Common fixed points of R-weakly commuting maps in generalized metric spaces Fixed Point Theory and Applications 2011 2011:41 Page 11 of 11 ...

Ngày tải lên: 21/06/2014, 00:20

... generated by (1.5) converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone ... Bunyawat and Suantai Fixed Point Theory and Applications 2011, 2011:47 http://www.fixedpointtheoryandapplications.com/content/2011/1/47 Page of 13 for all y Î C The set of solutions of the variational ... [6], we introduced the following iteration to find some solutions of variational inequality and fixed points of countable family of nonexpansive mappings in a Hilbert spaces H: x0 Î C, xn+1 = PC...

Ngày tải lên: 21/06/2014, 00:20

... We denote by F(S ) the set of all common fixed points of mappings in S (S), i.e., F(S ) := s∈s F(Ts ), where F (Ts) := {x Î C : Tsx = x} is the set of fixed points of Ts For any bounded net {xa} ... article as: Anakkamatee and Dhompongsa: Rodé’s theorem on common fixed points of semigroup of nonexpansive mappings in CAT(0) spaces Fixed Point Theory and Applications 2011 2011:34 Submit your manuscript ... and Dhompongsa Fixed Point Theory and Applications 2011, 2011:34 http://www.fixedpointtheoryandapplications.com/content/2011/1/34 Page of 14 Further, for each x Î C, the limit point of {Tμα x}is...

Ngày tải lên: 21/06/2014, 01:20

... problem of finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed points of a family of infinitely nonexpansive mappings and the set of solutions of ... for finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of ... family of infinitely (finitely) nonexpansive mappings is too completed to use for finding the common element of the set of solutions of problem (1.2) and the set of fixed points of a family of infinitely...

Ngày tải lên: 21/06/2014, 02:20

... converges strongly to x∗ The rest of the proof is almost the same as Theorem 3.1 This completes the proof Remark 3.3 Theorems 3.1 and 3.2 improve and generalize Theorem 3.1 of from contractive mapping ... supported by The Key Program of NSFC Grant no 70831005 , the National Natural Science Foundation of China 10671135, 11026063 , and the Open Fund PLN0904 of State Key Laboratory of Oil and Gas Reservoir ... family of nonexpansive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol 323, no 2, pp 1402–1416, 2006 R Chen and H He, “Viscosity approximation of common fixed points...

Ngày tải lên: 21/06/2014, 07:20

... set of fixed points of f resp., g is denoted by F f resp., F g A point x ∈ M is a coincidence point common fixed point of f and g if fx gx x fx gx The set of coincidence points of f and g is denoted ... have U f U ∪ g 0c0 , 3.19 Journal of Inequalities and Applications then by the definition of f, we can consider U ⊆ 0, Hence closure of U being closed subset of a compact set is compact Also pn ... f k a Journal of Inequalities and Applications a Thus a is a common fixed point of f k and g k and hence of f a contradiction, hence f k a and g Now we establish the uniqueness of a Suppose there...

Ngày tải lên: 21/06/2014, 07:20

... fixed point p of {Tm }, m ∈ {1, 2, } such that p is the unique solution, in F, to the variational inequality f p − p, J y − p ≤ 0, ∀y ∈ F 3.3 Proof Step We prove the uniqueness of the solution ... of T , where p is the unique solution in F T to the following variational inequality: f p − p, j u − p ≤ ∀u ∈ F T 3.19 Acknowledgment A Razani would like to thank the School of Mathematics of ... Analysis Fixed Point Theory and Its Applications, Yokohama, Yokohama, Japan, 2000 Z B Xu and G F Roach, “Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces,” Journal of...

Ngày tải lên: 21/06/2014, 11:20

... at each of two antipodal points The embedding induces a monomorphism of homology The map fP has been defined so that pfP −x and therefore fP induces a map if x, −x are antipodal points of S2 , ... References S W Kim, R F Brown, A Ericksen, N Khamsemanan, and K Merrill, Fixed points of maps of a nonaspherical wedge,” Fixed Point Theory and Applications, vol 2099, Article ID 531037, 18 pages, ... 2-sphere in X Therefore the image of gP ∗ : H2 S2 , Z/2Z → H2 X, Z/2Z would be either trivial or a single generator of H2 X, Z/2Z On the other hand, the image of fP ∗ in H2 X, Z/2Z is nontrivial...

Ngày tải lên: 21/06/2014, 11:20

... subsequence {xnk } of {xn } is convergent to an element of A Denote N M a collection of all nonempty subsets of M, C M a collection of all nonempty closed subsets of M and K M a collection of all nonempty ... subsets of M An element x ∈ M is said to be an endpoint of a set-valued map T : M → N M , if T x {x} We denote a set of all endpoints of T by End T An element x ∈ M is said to be a fixed point of ... The remaining is same as the proof of Theorem 2.5 References L.-G Huang and X Zhang, “Cone metric spaces and fixed point theorems of contractive mappings,” Journal of Mathematical Analysis and Applications,...

Ngày tải lên: 21/06/2014, 20:20

... coincidence points of R-weakly commuting maps,” International Journal of Mathematics and Mathematical Sciences, vol 26, no 3, pp 179–182, 2001 21 G Jungck and B E Rhoades, Fixed points for set valued functions ... S K Nigam, Fixed point theorems for hybrid contractions,” Var¯ hmihir Journal of Mathematical Sciences, vol 2, no 2, pp 275–281, 2002 a 19 A Azam and I Beg, “Coincidence points of compatible ... common fixed point Fixed Point Theory and Applications Proof Note that M x, y ≤ α β γ max d fx, gy , d fx, T x , d gy, Sy , δ fx, Sy , δ gy, T x 2.11 So, 2.9 is a special case of 2.1 and hence...

Ngày tải lên: 21/06/2014, 20:20

... studied in 7, 9–14 Fixed Point Theory and Applications Recently, a problem of finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively ... > for Proof Step {xn } is well defined This step is almost the same as Step of the proof of Theorem 3.3, so it is omitted Step {xn } is a Cauchy sequence in C We can follow the proof of Theorem ... Proof The proof of this lemma can be extracted from that of Lemma 1.8; so it is omitted If E has a stronger assumption, we have the following lemma Lemma 1.8 Let C be a closed convex subset of...

Ngày tải lên: 21/06/2014, 20:20

... 2 Fixed Point Theory and Applications bound of a subset A of X if x ≤ b for each x ∈ A If b ∈ A, we say that b is the greatest element of A, and denote b max A A lower bound of A and the ... gives a characterization of elements of the w-o chain of aG-iterations Lemma 2.3 Given G : X → X and a ∈ X, let C be the w-o chain of aG-iterations Then the elements of C have the following properties ... exists for all x ∈ X, then for each a ∈ X the maximum of the w-o chain of aG-iterations exists and is a fixed point of G Proof Let C be the w-o chain of aG-iterations The given hypotheses imply that...

Ngày tải lên: 21/06/2014, 20:20

... compactness of I yields that there exists a subsequence {Ank }k≥0 of {An }n≥0 satisfying that lim H Ank ,A = for some A ∈ I (2.18) k→∞ In view of (2.8), (2.18) and the nonexpansiveness of T, we ... [1] T Hu and J Huang, “Iteration of fixed points on hyperspaces,” Chinese Annals of Mathematics Series B, vol 18, no 4, pp 423–428, 1997 [2] L Deng, “Convergence of the Ishikawa iteration process ... Applications, vol 6, no 10, pp 1135–1141, 1982 [4] S Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space,” Proceedings of the American Mathematical Society, vol 59, no 1, pp...

Ngày tải lên: 21/06/2014, 22:20

... Hence, the set F of common fixed points of {Sn } and {Tn } is closed and so x∗ ∈ F This completes the proof of Theorem 2.1 Remark 2.2 Theorem 2.1 is a generalization and improvement of the corresponding ... conclusions of Theorem 2.1 for sequence {xn } defined by 2.39 still hold References F E Browder and W V Petryshyn, “Construction of fixed points of nonlinear mappings in Hilbert space,” Journal of Mathematical ... conclusion of Theorem 2.4 can be obtained from Theorem 2.1 immediately This completes the proof of Theorem 2.4 Theorem 2.5 Let E be a real Banach space, let C be a nonempty closed convex subset of E,...

Ngày tải lên: 21/06/2014, 23:20

... References B Halpern, Fixed points of nonexpanding maps,” Bulletin of the American Mathematical Society, vol 73, no 6, pp 957–961, 1967 R Wittmann, “Approximation of fixed points of nonexpansive mappings,” ... fixed points of families and semigroups of nonexpansive mappings,” Nonlinear Analysis: Theory, Methods & Applications In press 19 A T Lau, H Miyake, and W Takahashi, “Approximation of fixed points ... amenability of Banach algebras,” Journal of Mathematical Analysis and Applications, vol 344, no 2, pp 942–955, 2008 43 A T Lau and Y Zhang, Fixed point properties of semigroups of nonexpansive...

Ngày tải lên: 21/06/2014, 23:20

... “Approximating fixed points of nonexpansive mappings,” Proceedings of the American Mathematical Society, vol 44, no 2, pp 375–380, 1974 15 J Schu, “Iterative construction of fixed points of strictly pseudocontractive ... Proceedings of the American Mathematical Society, vol 4, no 3, pp 506–510, 1953 S Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space,” Proceedings of the American ... F T1 ∩ F T2 ∩ F T3 / ∅ and one of T1 , T2 , and T3 is demicompact, then {xn } converges strongly to a common fixed point of T1 , T2 , and T3 Proof Without loss of generality, we may assume that...

Ngày tải lên: 21/06/2014, 23:20

... fixed point of S and T This completes the proof of the theorem Acknowledgment The work was partially supported by the Emphases Natural Science Foundation of Guangdong Institution of Higher Learning, ... pair of mean nonexpansive with a nonempty common fixed points set; if b > 0, < α ≤ αn ≤ 1/2, ≤ βn ≤ β < 1, then the Ishikawa sequence {xn } converges to the common fixed point of S and T Proof First, ... common fixed points of nonexpansive mappings in Hilbert e spaces,” Journal of Mathematical Analysis and Applications, vol 325, no 1, pp 469–479, 2007 R A Rashwan, “On the convergence of Mann iterates...

Ngày tải lên: 22/06/2014, 00:20

... function for γf i.e., h x Journal of Inequalities and Applications For finding a common element of the set of fixed points of nonexpansive mappings and the set of solution of the variational inequalities, ... point of nonexpansive mapping and strictly pseudocontractive mapping Moreover, we consider the problem of finding a common element of the set of fixed points of nonexpansive mapping and the set of ... } generated by 1.10 converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone...

Ngày tải lên: 22/06/2014, 02:20