[PDF] Top 20 Random fixed point theorems for asymptotic 1 set contraction operators

... < 1, such that for each nonempty bounded subset A of K , we have α(T (A)) ≤ kα(A) , then T is called a k -set ...= 1, then T is called a 1-set ...-set contraction map ... See full document

... of random nonlinear operators and their properties and is much needed for the study of various classes of random ...equations. Random techniques have been crucial in diverse areas from ... See full document

... a fixed point in ...Takahashi’s fixed point theorem is a real generalization of Nadler’s fixed point ...(1989) fixed point theorem as well as Klim and Wardowki ... See full document

... Random fixed point theorems for contraction mappings in polish spaces and random fixed point theorems are of fundamental importance in probabilistic ... See full document

... nonlinear operators and their properties and is much needed for the study of various classes of random equa- ...on fixed points of non-expansive mappings, contractive mappings in differ- ent spaces ... See full document

... Probabilistic metric spaces originated in 1942 by Karl Menger [1]. The notion of Menger was to replace non-negative real numbers with distribution functions as the values of the metric. An analogy between ... See full document

... the set-valued contractions defined on product spaces when the underlying space is a complete metric space endowed with a ...fixed point results for the so-called set-valued G-Preši´c operators ... See full document

... To set up our results in the next section we recall some definitions and ...[0, 1] × [0, 1] ® [0, 1] is called a continu- ous t-norm if ([0,1], *) is an abelian topological monoid with unit ... See full document

... al. 1 had proved the well-known KKM theorem on ...some fixed point theorems for this ...the fixed point theorems for a weaker Meir- Keeler type ψ -set ... See full document

... middle point linear operators, which are defined in Definition ...convex operators in the sense of ...affine operators. However, as shown in Example 3.3, middle point linear ... See full document

... 0, 1. The best proximity point is some z ∈ A ∪ B such that dz, Tz distA, ...a fixed point of T since distA, B 0 11–13. If k 1, then dTx, Ty ≤ dx, y; ∀x ∈ A, ∀y ∈ B and T : A ∪ B → A ∪ B ... See full document

... new fixed point theorems for semi-closed 1- set-contractive operators and existence theorems of solutions for the equation Ax = μx which generalize a great deal of ... See full document

... new operators, namely, convex- power 1-set-contraction operators in Banach spaces, and study the existence of fixed points of this class of ...by operators, we obtain ... See full document

... Subsequently many extensions and generalizations of Theorem 1.2 appeared (see, for instance, [1–3, 5–13, 16, 18–23, 26, 27]). Underlying the power and importance of this new class of maps, Briseid [5, 7] has ... See full document

... Fixed point theory has the diverse applications in different branches of mathematics, statistic, engineering, economics and many other ...science. Random fixed point theory is very ... See full document

... monotone operators in partially ordered Banach spaces requires compactness, continuity or concavity-convexity of the ...uniqueness theorems of positive fixed point of e-concave-convex mixed ... See full document

... We introduce a new nonlinear mapping similar to the nonspreading mapping which is defined by Kohsaka and Takahashi (Arch. Math. 91:166-177, 2008). We prove fixed point theorems for such a mapping without the ... See full document

... Then F and g have a unique coupled coincidence point (u, v), with F(u, v) = u = v = F(v, u). Corollary . Consider (X, G) to be a G-metric space endowed with an -distance called . Let F : X × X → X and g : X → X ... See full document

... monotone operators were introduced by Guo and Lakshmikantham in 1 in ...of operators in Banach spaces and obtained a lot of interesting and important ...uniqueness theorems of positive ... See full document

... Banach contraction principle appears everywhere in mathematics: Analysis, geom- etry, statistics, graph theory, and logic programming are some of the fields in which the Banach contraction principle and/or ... See full document