báo cáo hóa học: " The fixed point theorems of 1-set-contractive operators in Banach space" docx

... defined the fixed point index of 1-set- contractive operators and obtained some fixed point theorems of 1-set-contractive opera- tors. Recently, Li [6] obtained some fixed point theorems for 1-set-contractive ... Wang: The fixed point theorems of 1-set-contractive operators in Banach space. Fixed Point Theory and Applications 2011 2011:15. Wan...

Ngày tải lên: 21/06/2014, 02:20

... and the proof is completed. □ For a metric space (X, d), we will denote by Cl(X) the set of all closed subsets of X. In view of proving Lemma 2.3, we can obtain a fixed point theorem in the general metric ... y ), since c>1. This fact implies that the Banach contraction principle cannot be used for guaranteeing the existence of fixed point of our considere...

Ngày tải lên: 20/06/2014, 22:20

... point of f if fx = x. The set of all fixed points of f is denoted by F(f). A point x Î M is called a coincidence point of f and T if fx = Tx.Weshallcallw = fx = Tx a point of coincidence of f ... A point x Î M is called a common fixed point of f and T if x = fx = Tx.L etC(f, T), PC(f, T), and F(f, T) denote the sets of all coincidence points, points of co...

Ngày tải lên: 20/06/2014, 22:20

... nonlinear contraction, fixed point, coincidence point, coincidence fixed point, partially ordered set, altering distance function 1. Introduction and Preliminaries Generalization of the Banach ... for a pair of weakly increasing mappings with respect to another map. The aim of this article is to study new coincidence point theo rems for a pair of weakly decreasing mappi...

Ngày tải lên: 20/06/2014, 22:20

... spaces is introduced, and some coincidence and common fixed- point theorems for these contractions are proved. Presented theorems are twofold generalizations of very recent fixed- point theorems of Altun ... partial metric fixed- point theory. The aims of this paper is to establish coincidence and common fixed- point theorems in ordered partial metric spaces with...

Ngày tải lên: 20/06/2014, 22:20

... y, z Î X. Then f, g, and h have a common fixed point in X. Moreover, any fixed point of f is a fixed point g and h and conversely. Proof. Suppose x 0 is an arbitrary point in X.Define{x n }byx 3n+1 = ... continuity and commutativity of any mappings involved therein. We also introduce the notation of a generalized probabilistic metric space and obtain common fixed...

Ngày tải lên: 20/06/2014, 22:20

... =∅. Proof. Proof is similar to Theorem 2.2(i), instead of applying Theorem 2.1,weapply Theorem 3.5.  N. Hussain and V. Berinde 3 In 1963, Meinardus [10] employed the Schauder fixed point theorem to ... monotone [4]. Following the arguments of Jungck [8, Theorem 3.2] and using Theorem 2.1 instead of Theorem 3.1 of Jungck [8], we obtain, Theorem 3.5. Let T and f be continuous s...

Ngày tải lên: 22/06/2014, 22:20

... y n || ) Saejung et al. Fixed Point Theory and Applications 2011, 2011:26 http://www.fixedpointtheoryandapplications.com/content/2011/1/26 Page 8 of 11 RESEARC H Open Access Another weak convergence theorems ... doi:10.1016/0362-546X(91) 90200-K 7. Browder, FE: Nonlinear operators and nonlinear equations of evolution in Banach spaces. Nonlinear functional analysis. Proceedings...

Ngày tải lên: 21/06/2014, 01:20

... T n+1 f) ≤ L n+1 <∞ for all n Î N.Bythe fixed- point alternative, there exists a natural number n 0 such that the mapping F is the unique fixed point of T in the set  = {g ∈ |d(T n 0 f , g) < ... ∞. (2:10) Applying the alternative of fixed point, we see that there exists a fixed point F of T in Ω such that F( x , y) = lim n→∞ 4 n f  x 2 n , y 2 n  for...

Ngày tải lên: 20/06/2014, 22:20

... ≤ L | m | . By Theorem 2.2, there exists a mapping A : X ® Y satisfying the following: (1) A is a fixed point of J, that is, A  x m  = 1 m A(x ) (5) for all x Î X. The mapping A is a unique fixed point of ... Theorem 2.2, there exists a mapping A : X ® Y satisfying the following: (1) A is a fixed point of J, that is, A  x m  = 1 m A(x ) (12) for all x Î X. The ma...

Ngày tải lên: 20/06/2014, 22:20