[PDF] Top 20 On monotone pointwise contractions in Banach spaces with a graph

... G-monotone pointwise Lipschitzian mapping, then it is not necessarily continuous by contrast to the case of pointwise Lipschitzian ...of pointwise contraction, we ... See full document

... They assumed that f satisfies a contraction condition not necessarily for all x and y, but for those such that x ≤ y. Their result was generalized by Nieto and Rodríguez-López [, ] who weakened the continuity and the ... See full document

... the graph G(A) of A are defined by D(A) = {x ∈ X : Ax = ∅}, R(A) = x∈X Ax, and G(A) = {(x, x ∗ ) ∈ X × X ∗ : x ∗ ∈ Ax } , ...be monotone if x – y, x ∗ – y ∗ ≥  whenever (x, x ∗ ), (y, y ∗ ) ∈ ...maximal ... See full document

... In this paper, we study the case of nonexpansive mappings defined in Banach spaces endowed with a graph. Nonexpansive mappings are those which have Lipschitz constant equal to . The fixed point theory ... See full document

... real Banach space and C a nonempty subset of ...the graph of A, that is, G(A) = f (x, x*) Î E × E* : x* Î ...be monotone if 〈 x* - y*, x - y 〉 ≥ 0 whenever (x, x*); (y, y*) Î ...maximal ... See full document

... Example  Let K be a bounded closed convex subset of the Hilbert space  . Let F : K → K. In [] it is shown that if F is defined and continuously Fréchet differentiable on a convex open set containing K, then F is a ... See full document

... metric spaces endowed with a ...directed graph such that the set V(G) of its ver- tices coincides with X and ⊆ E(G), where E(G) is the set of edges of the ...a Banach G-contraction (see Definition ... See full document

... For the particular case of a single-valued operator t : X → X the above notations should be considered accordingly. In particular, the condition E(G) ∈ I(t × t) means that the op- erator t is edge preserving (in the ... See full document

... of Banach states that if (X, d) is a complete metric space and f : X → X such that d(f (x), f (y)) ≤ αd(x, y) for all x, y ∈ X, where α ∈ [, ), then f has a unique fixed ...The Banach fixed point theorem ... See full document

... Remark . In the classical Banach contraction principle, the metric space is not sup- posed to be bounded. In fact the contractive condition of the mapping implies that any orbit is bounded. In the case of a ... See full document

... uniform spaces in ...ric spaces endowed with a graph and generalized simultaneously the Banach contrac- tion principle from metric and partially ordered metric ...of contractions using ... See full document

... asymptotic pointwise contractions and asymptotic pointwise nonexpansive mappings in Banach spaces, while Hussain and Khamsi [] extended this result to metric spaces, and Khamsi ... See full document

... The Banach fixed point theorem for contraction mappings has been extended in many directions ...nonlinear contractions in partially ordered metric ... See full document

... the Banach contraction principle in partially ordered metric ...for monotone and generalized contractive type mappings in partially ordered metric ...mixed monotone and contraction mappings in ... See full document

... Proposition 2.2. Let X be a modular space with a graph G. If a mapping from X into itself satisfies (B1) (respectively, (B2)) for G, then it satisfies (B1) (respectively, (B2)) for G. In particular, a e ... See full document

... Banach’s contraction principle [] is remarkable in its simplicity, yet it is perhaps the most widely applied fixed point theorem in all of analysis. This is because the contractive con- dition on the mapping is simple ... See full document

... famous Banach contraction principle [9] has many applications in various branches of ...the Banach contraction principle is generalized by several authors (see, ...the Banach contraction principle in ... See full document

... asymptotic pointwise nonexpansive ...asymptotic pointwise contractions and asymptotic pointwise nonex- pansive mappings in Banach spaces, while Hussain and Khamsi [] extended ... See full document

... is monotone and u ∗ is a solution (when they exist) of the Hammerstein equation u + KFu = 0 if and only if (u ∗ , v ∗ ) is a zero point of A, where v ∗ = Fu ∗ ... See full document

... Theorem . Let (X, · ) be a Banach space and C ⊂ X be nonempty and bounded. Let F = {T (t); t ≥ } be a one-parameter semigroup of uniformly continuous mappings from C into C . Assume that F is strongly ... See full document