Báo cáo hóa học: " FIXED POINTS OF MULTIMAPS WHICH ARE NOT NECESSARILY NONEXPANSIVE" pdf
Báo cáo hóa học: " FIXED POINTS OF MULTIMAPS WHICH ARE NOT NECESSARILY NONEXPANSIVE" pdf
... χ(·).If T satisfiesT(x) ∩IC(x) =∅ ∀x ∈ C, (2.14)then T has a fixed point. FIXED POINTS OF MULTIMAPS WHICH ARE NOT NECESSARILY NONEXPANSIVENASEER SHAHZAD AND AMJAD LONEReceived 16 October 2004 ... remarked that the assumption of nonexpansivenessin the above theorem can not be avoided. In this paper, we prove a fixed point result for multimaps which are not necessarily nonexpansive. To ... Corporation Fixed Point Theory and Applications 2005:2 (2005) 169–176DOI: 10.1155/FPTA.2005.169170 Fixed points of multimaps 2. PreliminariesLet C beanonemptyclosedsubsetofaBanachspaceX.LetCB(X) denote...
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Báo cáo hóa học: " FIXED POINTS OF CONDENSING MULTIVALUED MAPS IN TOPOLOGICAL VECTOR SPACES" pot
... 108 Fixed points of condensing mapsFor a subset K of a topological vector space E, the closure, the convex hull, and theclosed convex hull of K in E are denoted by K,coK,andcoK, ... B of K such that F(B) is a relatively compact subset of B.NotethatC := coF(B)iscompactandC ⊂ B. In fact, since ψ is regular and c ≥ 1,it follows from ψ(coF(B)) ≤ cψ(F(B)) that ψ(coF(B)) = 0 which ... exists a nonempt y closed convex subset B of K such that F(B)isarelativelycom-pact subset of B.HenceC := coF(B) is compact, noting that the closed convex hull of acompact set in a Fr´echet space...
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Báo cáo hóa học: " FIXED POINTS AND COINCIDENCE POINTS FOR MULTIMAPS WITH NOT NECESSARILY BOUNDED IMAGES" pdf
... closed.Proof. The proof follows from Corollary 4.26 on taking S = I. 228 Fixed points and coincidence points Proposition 3.19. Suppose that A is a nonempty subset of X such that one of αA, ... thatd(u,v) ≤ ϕd(x, y). (4.6)Then F has a fixed point in X. FIXED POINTS AND COINCIDENCE POINTS FOR MULTIMAPS WITH NOT NECESSARILY BOUNDED IMAGESS. V. R. NAIDUReceived 20 August 2003 ... the collection of all nonempty,bounded subsets of X;CB(X) is the collection of all nonempty, bounded, closed subsets of X; S, T are self-maps on X; I is the identity map on X; F, G are mappings...
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Báo cáo hóa học: " FIXED POINTS AS NASH EQUILIBRIA" doc
... sufficienttorepeattheproof of B.) For this reason, we study conditions to assure that fixed points of a continu-ous function, or of a closed-graph correspondence, can be attained as Nash equilibria of a noncooperative ... exists a cor-respondence whose fixed points coincide with the equilibrium points of the game.However, it is natural to ask whether fixed points arguments are in fact necessarytools to guarantee ... generalization of Brouwer’s fixed point theorem, Duke Mathematical Journal 8(1941), no. 3, 457–459.[3] J. F. Nash, Equilibrium points in n-person games, Proceedings of the National Academy of Sci-ences of...
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Báo cáo hóa học: " FIXED POINTS AND CONTROLLABILITY IN DELAY SYSTEMS" potx
... solu-tion of (1.1)asafunctionofu(t) so that the behavior of the s ystem depends on (or iscontrolled by) the choice of u within a set U given in advance. Assume that two states of the system are given, ... [9]).AcknowledgmentThis research was supported in part by NSF of China (10471021).8 Fixed points and controllability in delay systemswhere Cijis the cofactor of wi,wj in the mat rix (wi,wj)n×n,and1|α|≤|a|≤2|α|for ... over half of a century. A large number of applications have appeared in biology, medicine, economics, engineering, and informa-tion technology. Many actual systems have the property of “after-effect,”...
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Báo cáo hóa học: " FIXED POINTS, PERIODIC POINTS, AND COIN-TOSSING SEQUENCES FOR MAPPINGS DEFINED ON TWO-DIMENSIONAL CELLS" docx
... compactsubsets of are those subsets of which are closed relatively to , or, that is the samesince X is a Hausdorff space, the closed sets of X which are contained in .We denote ∂⊆ = ... some theorems on the existence of fixed points, periodic points, and sequences of iterates which are chaotic in a suit-able manner. Our results, motivated by the study of the Poincar´e map associated ... invited to provide a proof of this claimed equivalence.We notice that (Ᏸ,ψ):Ꮽ Ꮾ does not imply that ψ(Ᏸ) ⊆ Ꮾ.However,wedohaveψ() ⊆ Ꮾ. FIXED POINTS, PERIODIC POINTS, AND COIN-TOSSINGSEQUENCES...
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Báo cáo hóa học: " FIXED POINTS, STABILITY, AND HARMLESS PERTURBATIONS" pdf
... space of bounded continuous functions which agree with ψ and use the above equation for x to define a mapping. That mapping wouldbe a contraction because of (3.32). We would complete the proof as ... ∞ . (2.10)In all of these, f (x) ≥ 0andxg(x) ≥ 0. All of these problems bear out the conjecture thatthe functions in (1.1) represent a harmless pertur bation.All of these are important classical ... comparison, Fixed Point Theory 4(2003), no. 1, 15–32.[7], Stability by fixed point methods for highly nonlinear delay equations, Fixed Point Theor y5 (2004), no. 1, 3–20.[8], Fixed points and...
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Báo cáo hóa học: " Down-regulation of cell surface CXCR4 by HIV-1" pdf
... surfaceexpression of CD3 indicating that decreased expression of CXCR4 is not a non-specific consequence of HIV-1 infec-tion (not shown).HIV-1 infection induces internalization of CXCR4 in RH9 ... http://www.virologyj.com/content/5/1/6Page 5 of 10(page number not for citation purposes)Immunofluorescence microscopy analysis of CXCR4 expression in permeabilized HIV-1 and mock infected RH9 cellsFigure 3Immunofluorescence ... Immunofluorescence staining control with isotype-matched monoclonal antibody. Panel C: CXCR4 immunofluores-cence staining of H9 cells. Panels E and G, CXCR4 immunofluorescence staining of HIV-1...
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Báo cáo hóa học: " Solving systems of nonlinear matrix equations involving Lipshitzian mappings" pdf
... A*F(X)A.SuchproblemwasstudiedbyLiaoetal.[15].Now,weintroducethefollowingdefinition.Berzig and Samet Fixed Point Theory and Applications 2011, 2011:89http://www.fixedpointtheoryandapplications.com/content/2011/1/89Page 2 of 10RESEARC H Open AccessSolving systems of nonlinear ... iterative method, fixed point, Thompson metric1 Introduction Fixed point theory is a very attractive subject, which has recently drawn much atten-tion from the communities of phy sics, engineering, ... (12).Berzig and Samet Fixed Point Theory and Applications 2011, 2011:89http://www.fixedpointtheoryandapplications.com/content/2011/1/89Page 6 of 10where q3= 1/6.Proof. Follows from Propositions...
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Báo cáo hóa học: "BASIC PROPERTIES OF SOBOLEV’S SPACES ON TIME SCALES" pdf
... (4.8)14 Basic properties of Sobolev’s spaces on time scales[6] E. Hewitt and K. Stromberg, Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable, 3rd ed., ... point of J is isolated.Proof. Denote by Ᏺpthe closed unit ball in W1,pΔ(J); we know from Theorem 3.4 that Ᏺpis closed and bounded in C(J).If p>1, then the fundamental theorem of Calculus ... +i∈Iσti−ti·δti, if M ∈ T,(2.1)where{ti}i∈I, I ⊂ N, is the set of all right-scattered points of T, M is the supremum of T, λis the Lebesgue measure, δtiis the Dirac measure concentrate...
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