... is said to be maximal monotone if it is not properly contained in any other monotone operator Equivalently, M is maximal monotone if R I rM H for all r > For a maximal monotone operator M on ... 2 FixedPoint Theory and Applications Let A : C → H be a mapping Recall that A is said to be monotone if Ax − Ay, x − y ≥ 0, ∀x, y ∈ C 1.3 A is said to be inverse strongly monotone if there ... defined by R M x∈H Mx is said to be the range of M The set G M defined by G M { x, y ∈ H × H : x ∈ D M , y ∈ R M } is said to be the graph of M Recall that M is said to be monotone if x − y, f − g >...
... 1.4 It is easy to know that I − T is − k /2 -inverse-strongly-monotone If k 0, then T is nonexpansive We denote by F T the fixed points set of T In 2003, for x0 ∈ C, Takahashi and Toyoda introduced ... following conditions: A1 F x, x for all x ∈ C; A2 F is monotone, that is, F x, y A3 for each x, y, z ∈ C, limt → F tz F y, x ≤ for all x, y ∈ C; − t x, y ≤ F x, y ; A4 for each x ∈ C, y → F x, y is ... is, for any x ∈ H, x − PC x ≤ x − y for all y ∈ C It is easy to see that PC is nonexpansive and u ∈ VI A, C ⇐⇒ u PC u − λAu , λ > 2.1 If A is an α-inverse-strongly monotone mapping of C to H,...
... BinDCT for inverse transform and original DCT for forward transform, then the differences between original data and recover data cannot be neglected It means that BinDCT cannot perform well to recover ... step is a biorthogonal transform, and its inverse transform also has similar lifting structures, which means we just need to subtract what was added at forward transform to invert a lifting step ... the floating -point multiplications result in the lifting steps are rounded to integers, as long as the same procedure is applied to both the forward and inverse transforms In order to implement...
... references therein A mapping S of C into itself is called nonexpansive if Su − Sv ≤ u − v , (1.4) for all u,v ∈ C We denote by F(S) the set of fixed points of S For finding an element of F(S) ∩ Ω under ... ⊂ H is closed and convex, a mapping S of C into itself is nonexpansive and a mapping A of C into H is α-inverse strongly monotone, Takahashi and Toyoda [7] introduced the following iterative ... (1.6) ∀n ≥ 0, where {λn } ⊂ [a,b] for some a,b ∈ (0,1/k) and {αn } ⊂ [c,d] for some c,d ∈ (0,1) Then the sequences {xn }, { yn } converge weakly to the same point PF(S)∩Ω (x0 ) Very recently,...
... constant to ensure a fixedpoint is also obtained Three fixedpoint theorems which extended the fixedpoint theory for Kannan mappings were stated and proved in [11] More attention has been paid to ... through fixedpoint theory of Caputo linear fractional systems has been provided in [30] Finally, promising results are being obtained concerning fixedpoint theory for multivalued maps (see, for ... converge to z and y for all x ∈ A , respectively, to y and z for all x ∈ B If A ∩ B ≠ ∅ then z = y ∈ A ∩ B is the unique fixedpoint of T : A ∪ B → A ∪ B Outline of proof: It is similar to that...
... T x, y − T y (9) for all x, y ∈ C Therefore, we can apply Theorem 3.2 to conclude that T has a fixed point, while the Aoyama–Iemoto–Kohsaka–Takahashi fixed point theorem fails to give us the desired ... 3.2 to conclude T has a fixed point, while both of the Browder FixedPoint Theorem and the Kohsaka–Takahashi fixed point theorem fail Proof It is easy to check that T is not nonexpansive As for ... point- dependent λ-hybrid relative to Df for some λ : C → R and is asymptotically regular with a bounded sequence {T n x0 }n∈N for some x0 ∈ C (5.3.4) The mapping x → f (x) for x ∈ X is weak -to- weak∗...
... equations: a fixed point approach FixedPoint Theory Appl 2008, Art ID 493751, pages (2008) [50] Radu, V: The fixed pointalternative and the stability of functional equations FixedPoint Theory 4, ... the fixed pointalternative J Math Anal Appl 306, 752–760 (2005) [48] Park, C: Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras FixedPoint Theory ... fixed point approach a Grazer Math Ber 346, 43–52 (2004) [41] C˘dariu, L, Radu, V: Fixedpoint methods for the generalized stability of functional equations in a a single variable Fixed Point...
... T x, y − T y (9) for all x, y ∈ C Therefore, we can apply Theorem 3.2 to conclude that T has a fixed point, while the Aoyama–Iemoto–Kohsaka–Takahashi fixed point theorem fails to give us the desired ... 3.2 to conclude T has a fixed point, while both of the Browder FixedPoint Theorem and the Kohsaka–Takahashi fixed point theorem fail Proof It is easy to check that T is not nonexpansive As for ... point- dependent λ-hybrid relative to Df for some λ : C → R and is asymptotically regular with a bounded sequence {T n x0 }n∈N for some x0 ∈ C (5.3.4) The mapping x → f (x) for x ∈ X is weak -to- weak∗...
... equations: a fixed point approach FixedPoint Theory Appl 2008, Art ID 493751, pages (2008) [50] Radu, V: The fixed pointalternative and the stability of functional equations FixedPoint Theory 4, ... the fixed pointalternative J Math Anal Appl 306, 752–760 (2005) [48] Park, C: Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras FixedPoint Theory ... fixed point approach a Grazer Math Ber 346, 43–52 (2004) [41] C˘dariu, L, Radu, V: Fixedpoint methods for the generalized stability of functional equations in a a single variable Fixed Point...
... fixed point are obtained By introducing a random iteration process with weak contraction random operator, we obtain a convergence theorem of the random iteration process to a random fixed pointfor ... random operator if for each ω ∈ Ω, such that for arbitrary x, y ∈ F we have T (ω, x) − T (ω, y) ≤ x − y (c) completely continuous random operator if the sequence {xn } in F converges weakly to x0 implies ... strongly to T (ω, x0 ) for each ω ∈ Ω (d) demiclosed random operator (at y) if {xn } and {yn } are two sequences such that T (ω, xn ) = yn and {xn } converges weakly to x and {T (ω, xn )} converges to...
... Kuaket, K, Kumam, P: Fixedpointfor asymptotic pointwise contractions in modular spaces Appl Math Lett 24, 1795–1798 (2011) 20 [24] Kumam, P: On uniform opial condition, uniform Kadec–Klee property ... y)) (3.13) for all x, y ∈ Xw and for all λ > 0, where k ∈ [0, ), then T has a unique fixed point in Xw Moreover, for any x ∈ Xw , iterative sequence {T n x} converges to the fixed point Proof ... , x) 2 for all λ > and for each n ∈ N Taking n → ∞ in (3.3) implies that wλ (T x, x) = for all λ > and thus T x = x Hence, x is a fixed point of T Next, we prove that x is a unique fixed point...
... c Ume, JS: Fixedpoint theorems related to Ciri´ contraction principle J Math Anal Appl 225, 630–640 (1998) Beg, I, Azam, A, Arshad, M: Common fixed points for maps on topological vector space ... Topological vector space-valued cone metric spaces and fixed c c c point theorems FixedPoint Theory Appl 2010, Article ID 170253, 17 (2010) doi:10.1155/2010/170253 11 Abbas, M, Rhoades, BE: Fixed ... (iii) and (iv) Fixedpoint theorems for w-cone distance contraction mappings in K-metric spaces We note that the method of Du [2] for cone contraction mappings cannot be applied for a w-cone distance...
... Petrot FixedPoint Theory and Applications 2011, 2011:78 http://www.fixedpointtheoryandapplications.com/content/2011/1/78 Cho, YJ, Hirunworakit, S, Petrot, N: Set-valued fixed points theorems for ... Common fixedpoint theorem for hybrid generalized multivalued Thai J Math 9(2), 417–427 (2011) 11 Ume, J-S: Existence theorems for generalized distance on complete metric spaces FixedPoint Theory ... Some fixedpoint theorems for contractive multi-valued mappings induced by generalized distance in metric spaces FixedPoint Theory and Applications 2011 2011:78 Submit your manuscript to a journal...
... lim xn+1 = lim Txn = Tz n→∞ n→∞ and, therefore, z is a fixedpoint of T Harjani et al FixedPoint Theory and Applications 2011, 2011:83 http://www.fixedpointtheoryandapplications.com/content/2011/1/83 ... comparable to themselves Moreover, (1,0) ≤ T(1, 0) = (1, 0) and the operator T has two fixed points In what follows, we present a sufficient condition for the uniqueness of the fixedpoint in Theorems ... xn(k0 )+1 = T(xn(k0 ) ) , and xn(k0 ) = z is a fixedpoint of T Suppose that for any k Î N, xn(k)
... point of T Finally, to prove the uniqueness of the fixed point, we have y, z Î X with y and z fixed points of T The cyclic character of T and the fact that y, z Î X are fixed points of T, imply ... Accepted: 27 October 2011 Published: 27 October 2011 References Kirk, WA, Srinivasan, PS, Veeramani, P: Fixed points for mappings satisfying cyclical weak contractive conditions FixedPoint Theory ... FixedPoint Theory Appl 2008 (2008) Article ID 406368 doi:10.1186/1687-1812-2011-69 Cite this article as: Karapinar and Sadarangani: Fixedpoint theory for cyclic (j - ψ)-contractions Fixed Point...
... Simsek, H: Some fixedpoint theorems on ordered metric spaces and application FixedPoint Theory Appl 2010, 17 (2010) (Article ID 621469) Altun, I, Erduran, A: Fixedpoint theorems for monotone mappings ... metric fixed- point theory The aims of this paper is to establish coincidence and common fixed- point theorems in ordered partial metric spaces with a function satisfying the condition (t)
... Chen FixedPoint Theory and Applications 2011, 2011:72 http://www.fixedpointtheoryandapplications.com/content/2011/1/72 In 1989, Mizoguchi-Takahashi [4] proved the following fixedpoint theorem ... d(x, y) for all x, y Î X, where ξ : [0, ∞) ® [0, 1) satisfies lim sups→t+ ξ (s) < 1for all t Î [0, ∞) Then, T has a fixedpoint in X In the recent, Amini-Harandi [5] gave the following fixedpoint ... only if x = y = In [6,7], the authors proved some fixedpoint results for the C-contractions In this section, we present some fixedpoint results for the weakly ψ-C-contraction in complete metric...