thévenin s theorem and norton s theorem

... Caristi s fixed point theorem and the results in the studies of Jachymski, Feng and Liu, Khamsi, and Li MSC 2010: 06A06; 47H10 Keywords: maximal and minimal point; Caristi s fixed point theorem; Caristi-type ... problem stated by Kirk First, several existence theorems of maximal and minimal points are established By using them, some generalized Caristi s fixed point theorems are proved, which improve Caristi s ... In the past decades, Caristi s fixed point theorem has been generalized and extended in several directions, and the proofs given for Caristi s result varied and used different techniques, we refer...

Ngày tải lên: 18/06/2014, 22:20

... Caristi s fixed point theorem and the results in the studies of Jachymski, Feng and Liu, Khamsi, and Li MSC 2010: 06A06; 47H10 Keywords: maximal and minimal point; Caristi s fixed point theorem; Caristi-type ... problem stated by Kirk First, several existence theorems of maximal and minimal points are established By using them, some generalized Caristi s fixed point theorems are proved, which improve Caristi s ... In the past decades, Caristi s fixed point theorem has been generalized and extended in several directions, and the proofs given for Caristi s result varied and used different techniques, we refer...

Ngày tải lên: 20/06/2014, 04:20

... the assumptions made on h in [12,13] force that (H) is satisfied In other words, (H) is necessarily assumed in [12-14] Meanwhile,  is always assumed to be lower semicontinuous there In this study, ... ε} for some ε >0 Assume that  is lower semit∈X continuous and bounded below, h is continuous and nondecreasing, and there exists δ >0 and c >0 such that h(t) ≥ ct for each t Î [0, δ] He showed ... In what follows we shall show that Theorem implies Caristi s fixed point theorem The following lemma shows that there does exist some partial order ≼ on X such that (H3) is satisfied Lemma Let...

Ngày tải lên: 20/06/2014, 21:20

... Coincidence and fixed point theorems in S- KKM class All topological spaces are supposed to be Hausdorff Let X and Y be two topological spaces A multimap T : X → 2Y is said to be (a) upper semicontinuous ... a closed subset of X × Y Lemma 2.1 (Lassonde [9, Lemma 1]) Let X and Y be two topological spaces and T : X Y (a) If Y is regular and T is u .s. c with closed values, then T is closed Conversely, ... Y is compact and T is closed, then T is u .s. c with closed values (b) If T is u .s. c and compact-valued, then T(A) is compact for any compact subset A of X Let X be a subset of a vector space and...

Ngày tải lên: 22/06/2014, 22:20

... of Landau s theorem using Rado s theorem The necessity of (1) is obvious Now assume that (1) holds Let X = {(i, j); ≤ i, j ≤ n, i = j} Consider the matroid M on X whose circuits are the n disjoint ... integers r1 , r2 , , rn , it is possible to use Rado s theorem to establish necessary and sufficient conditions for T to be extendable to a tournament T with score sequence r1 , r2 , , rn Thus ... University Press, New York, 1992 [7] K.B Reid, Tournaments: scores, kings, generalizations and special topics, Congressus Numerantium, 115 (1996), 171–211 [8] C Thomassen, Landau s characterization...

Ngày tải lên: 07/08/2014, 21:21

... exists x ∈ C such that {T n x}n∈N is bounded; (b) T has a fixed point Obviously, T is nonexpansive if and only if it is 0-hybrid; T is nonspreading if and only if it is 2-hybrid; T is hybrid if and ... be a l .s. c strictly convex function so that it is Gˆteaux differentiable on Int(D) and a is bounded on bounded subsets of Int(D) Suppose C ⊆ Int(D) is a nonempty closed convex subset of X and T ... h(y) is always less than or equal to zero and we have proved that Df (T x, T y) − Df (x, y) ≤ for all x, y ∈ [0, 0.85] Weak convergence theorems In this section, we discuss the demiclosedness and...

Ngày tải lên: 18/06/2014, 22:20

... exists x ∈ C such that {T n x}n∈N is bounded; (b) T has a fixed point Obviously, T is nonexpansive if and only if it is 0-hybrid; T is nonspreading if and only if it is 2-hybrid; T is hybrid if and ... be a l .s. c strictly convex function so that it is Gˆteaux differentiable on Int(D) and a is bounded on bounded subsets of Int(D) Suppose C ⊆ Int(D) is a nonempty closed convex subset of X and T ... h(y) is always less than or equal to zero and we have proved that Df (T x, T y) − Df (x, y) ≤ for all x, y ∈ [0, 0.85] Weak convergence theorems In this section, we discuss the demiclosedness and...

Ngày tải lên: 20/06/2014, 04:20

... Authors’ contributions L-JL responsible for problem resign, coordinator, discussion, revise the important part, and submit C-SC is responsible for the important results of this article, discuss, and ... conclusion of Theorem 3.1 is still true if S: C ® C is a quasi-nonexpansive mapping, and I - S is demiclosed at zero, that is, xn ⇀ x and (I - S) xn ⇀ implies that (I - S) x = In Theorem 3.1, if S ... times of iteration process for Theorem 3.2 is much than ones in Theorem 3.1 (ii) The conclusion of Theorem 3.2 is still true if S: C ® C is a quasi-nonexpansive mapping, and I - S is demiclosed...

Ngày tải lên: 20/06/2014, 21:20

... Authors’ contributions L-JL responsible for problem resign, coordinator, discussion, revise the important part, and submit C-SC is responsible for the important results of this article, discuss, and ... conclusion of Theorem 3.1 is still true if S: C ® C is a quasi-nonexpansive mapping, and I - S is demiclosed at zero, that is, xn ⇀ x and (I - S) xn ⇀ implies that (I - S) x = In Theorem 3.1, if S ... times of iteration process for Theorem 3.2 is much than ones in Theorem 3.1 (ii) The conclusion of Theorem 3.2 is still true if S: C ® C is a quasi-nonexpansive mapping, and I - S is demiclosed...

Ngày tải lên: 20/06/2014, 21:20

... nontrivial s- algebra of subsets of Ω Let P be a δ-ring of subsets of Ω, such that E ∩ A ∈ P for any E ∈ P and A Î Σ Let us assume that there exists an increasing sequence of sets Kn ∈ P such that ... mappings (in short KKM-mappings) in modular function spaces Then, we prove an analogue to Ky Fans fixed point theorem which can be seen as an extension to Brouwer s and Schauders fixed point theorems ... implies r(gn) ↓ As in the case of measure spaces, we say that a set A Î Σ is r-null if r(g1A) = for every g ∈ E A property holds r-almost everywhere if the exceptional set is r-null As usual...

Ngày tải lên: 20/06/2014, 22:20

... metric spaces with nonnormal cones We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known ... space and its cone is not normal, neither of the mentioned results from 7–10, 14 can be used to obtain such conclusion Thus, Theorem 3.1 and its corollaries are proper extensions of these results ... endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces,” Fixed Point Theory and Applications, vol 2010,...

Ngày tải lên: 21/06/2014, 11:20

... processes for the class of mappings which is not necessarily Lipschitzian Moreover, a strong convergence theorem was also established in a real Hilbert space by hybrid projection methods; see ... pseudocontractions was introduced by Qihou in 1996 see also Kim and Xu studied weak and strong convergence theorems for this class of mappings It is important to note that every asymptotically κ-strict pseudocontractive ... class of mappings which are asymptotically nonexpansive in the intermediate sense contains properly the class of asymptotically nonexpansive mappings Recall that T is said to be a κ-strict pseudocontraction...

Ngày tải lên: 21/06/2014, 11:20

... This is why the above theorems were stated in terms of {Lip T n } Using the ideas described above one can prove fixed point results for mappings which contracts orbits and obtain similar results ... Theory and Applications Basic Definitions and Results First let us start by making some basic definitions Definition 2.1 Let E be a real Banach space with norm called a cone if and only if · and P a subset ... points f, g, h ∈ X In the next result we consider the case of metric type spaces X, D when D satisfies Recall that a subset Y of X is said to be bounded whenever sup{D x, y ; x, y ∈ Y } < ∞ Theorem...

Ngày tải lên: 21/06/2014, 17:20

... quasiadmissible Let A be an admissible subset of X Since G is an isometry, G−1 A is admissible and so is closed and acyclic Let A ⊆ X be closed, then A then G− A is compact Since G is continuous, ... A A is closed for each closed set A ⊆ M Let A A is admissible and so is acyclic 15, Lemma be an admissible subset of M Then I − A α A for each subset A of M, 5.2 Thus I is a quasiadmissible ... A is closed Hence Since F is upper semicontinuous and G A is closed, then H − A H is upper semicontinuous Now we show that H is condensing To show this, let A ⊆ M with α A > Since G− is 1-set...

Ngày tải lên: 21/06/2014, 23:20

... B, S, and T satisfy all conditions of 5, Theorem 2.4 and satisfy also all conditions of 5, Theorem 2.5 But the pairs A, S and B, T have no points of coincidence, and also the pairs A, S and ... a symmetric space X, d , in S and a point x ∈ X, limn→∞ d xn , x d-closedness implies τ d -closedness, and if d is a semimetric, the converse is also true At first, we prove coincidence point theorems ... satisfy additional conditions H.E and C.C Theorem 3.4 Let X, d be a symmetric(semimetric) space that satisfies (H.E) and (C.C) and let A, B, S, and T be self-mappings of X such that AX ⊂ T X and...

Ngày tải lên: 21/06/2014, 23:20

... proof of Theorem 2.1, we know that there exists subsequence {xnk } ⊂ {xn } such that xnk q ∈ K and satisfies 2.11 By the semicompactness of T , there exists a subsequence of {xnk } we still denote ... points of nonexpansive mapping and common fixed points of a finite family of nonexpansive mappings, respectively Now, we give some definitions and lemmas for our main results A Banach space E is said ... points of a finite family of nonexpansive mappings where Tn N {Ti }i in Banach spaces and also prove weak and strong convergence theorems Observe that if K is a nonempty closed convex subset of...

Ngày tải lên: 22/06/2014, 06:20

... topological space A subset D of X is said to be compactly closed (resp., compactly open) in X if for any compact subset K of X, the set D ∩ K is closed (resp., closed) in K Obviously, D is compactly ... has the following two properties (1) If Y is compact, then there exists y ∈ Y such that S (y) = φ (2) If X is compact, then there exists x ∈ X such that T(x) = φ Proof Case (1) Suppose Y is ... assumption (iv), T is closed Hence, all of the assumptions of Theorem 2.8 hold, and so there exists (μ,ν) ∈ X × Y such that ν ∈ T(μ) and μ ∈ F(ν), that is, f (μ,ν) ≥ a and p(μ,ν) < b Theorem 3.14 Let...

Ngày tải lên: 22/06/2014, 19:20

... consider the strong convergence concerning nonexpansive mappings in a Hilbert space For related results, see Moreau [11], and Kirk and Sims [6] Theorem 4.2 Let C be a nonempty closed convex subset ... is a continuous, strictly increasing, and convex function with g(0) = Then the properties of g yield that {un } is a Cauchy sequence Since E is complete and F(T) is closed, {un } converges strongly ... Main results In this section, we discuss the weak and strong convergence of (1.5) To prove our results, we need the following proposition Proposition 3.1 Let E be a uniformly convex and smooth...

Ngày tải lên: 23/06/2014, 00:20

... of ᏿, and if there exists some T (s) ∈ ᏿ which is semicompact, then {xn } converges strongly to a common fixed point of ᏿ S Atsushiba and W Takahashi 353 Acknowledgments This research was supported ... each s ∈ S and contains x0 = x So, without loss of generality, we may assume that C is bounded Fix ε > 0, t ∈ S and set M0 = sup{ z : z ∈ C } Then, from Proposition 2.2, there exists δ > such ... E into E∗ is single-valued and weakly sequentially continuous, then E satisfies Opial s condition Each Hilbert space and the sequence spaces p with < p < ∞ satisfy Opial s condition (see [8, 11])...

Ngày tải lên: 23/06/2014, 00:20

... fluctuation theorems are discovered which are in general valid for deterministic as well as for stochastic systems both in classical and quantum regimes In this thesis, we study quantum fluctuations of ... steady state for closed systems described by deterministic thermostated equations of motions [4–6, 17, 18] as well as for open systems modeled via stochastic differential equations [19–21] In this ... Fluctuation theorems Fluctuation theorems were first derived and formulated for classical systems The derivations were mostly based on the notion of classical trajectory picture The extension of these theorems...

Ngày tải lên: 08/09/2015, 19:39