[PDF] Top 20 Fixed point theorems for set-valued mappings on TVS-cone metric spaces

... The paper is organized as follows. In Section  some preliminary definitions and facts are given, while in Section , Bishop-Phelps’ and Caristi’s theorems are proved. Finally, Section  is devoted to an ... See full document

... (tvs)-cone metric spaces and prove various fixed point theorems for w -cone distance contraction mappings in tvs-cone metric ...our ... See full document

... convex cone if P + P ⊆ P and λP ⊆ P for λ ≥ . A convex cone P is said to be pointed (or proper) if P ∩ (–P) = { θ } ; and P is normal (or saturated) if E has a base of neighborhoods of zero consisting of ... See full document

... Chen, Some new fixed point theorems for set-valued contractions in complete metric spaces, Fixed Point Theory Appl. Liu, Common fixed point theorems for sequences of Φ -type contraction [r] ... See full document

... such metric spaces under the name cone metric spaces without mentioning the previous ...underlying cone. They also proved some fixed point theorem in such ... See full document

... Cone metric spaces were introduced by Huang and Zhang ...the set of real numbers by an ordered Banach space and obtained some fixed point theorems for mapping satisfying ... See full document

... Theorem 1.2 [3] Let (X , d) be a complete metric space, and F : X → Comp(X) is a multival- ued mapping, where Comp(X) is the set of all nonempty compact subsets of X . Assume that H(Fx, Fy) ≤ ϕ (d(x,y))d(x, ... See full document

... In this paper, we have established common fixed point results for Chatterjea-type con- tractive mappings in the context of complex-valued metric spaces. Our results may be the motivation ... See full document

... Fixed point theory plays one of the important roles in nonlinear ...famous fixed point theorem for contractive mappings in complete metric ...b-metric spaces ... See full document

... Remark 3.5. In 1 the authors gave an example of a map T which is contraction for d but not for the euclidian distance. From the above corollary, we see that LipT ≤ Kk. Since Kk may not be less than 1, then T may not be a ... See full document

... (f ) in Section ). For this reason, we have to state a scholastic definition of contraction. Definition . Let (X, d) be an algebraic cone metric space, and let F : X → X be a Lips- chitzian map with ... See full document

... normed spaces and cones have applications in applied mathematics, for instance, in using Newton’s approximation method 1–4 and in optimization theory ...K-normed spaces were introduced in the mid-20th ... See full document

... given cone , we defin e a Partial ordering ≤ on with respect to if and only if we shall write if , int P denotes the interior of ...The cone P is called regular if every increasing sequence which is bounded ... See full document

... fixed point theorem in the setting of a metric space, a b-metric space or a cone metric space cannot cope with Example ...fixed point theory of cone b-metric ... See full document

... of fixed points of functions satisfying certain contractive conditions has been at the center of vigorous research activity, for example see 1–5 and it has a wide range of applications in different areas such as ... See full document

... Common Fixed Point Theorems in TVS-Valued Cone Metric Spaces”, Presented at World Congress on Engineering, London July, 4-6, 2012, ...“Common fixed points of ... See full document

... of cone metric spaces CMSs by replacing real numbers with an ordering Banach ...of cone metric spaces but not contraction if considered over metric spaces and ... See full document

... of metric space by replacing the set of real numbers by ordered Banach space and defined cone metric space and extended Banach type fixed point theorems for contractive ... See full document

... d( f x, f y) αd(x, y) + β [d(x, f x) + d(y, f y)] + γ [d(x, f y) + d(y, f x)] (3.3) for all x, y ∈ X , where α , β , γ ≥ 0 and α + 2β + 2γ < 1. Then f has a unique fixed point in X . Proof. Set p ... See full document

... Fixed point theorems for multi-valued mappings in complete metric spaces, Math.. Common fixed points of two mappings, Pacific J.[r] ... See full document