begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

The first complete running time analysis of a stochastic divide and conquer algorithm was given for Quicksort, a sorting algorithm invented 1961 by Hoare. We analyse here the variant Random Median Quicksort. The analysis includes the expectation, the asymptotic distribution, the moments and exponential moments. The asymptotic distribution is characterized by a stochastic fixed point equation. T...

For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenetic trees. In this article, this statistic is studied under the Yule and uniform model of phylogenetic trees. The main tool of analysis is a coupling argument with another well-known index called the Sackin statistic. Asymptotics for the mean, variance and covariance of these two...

The Cluster Variation method is a class of approximation methods containing the Bethe and Kikuchi approximations as special cases. We derive two novel iteration schemes for the Cluster Variation Method. One is a fixed point iteration scheme which gives a significant improvement over loopy BP, mean field and TAP methods on directed graphical models. The other is a gradient based method, that is ...

Recently the author [Proc. Amer. Math. Soc. 103(1988), 11291135] proved random versions of an interesting theorem of Ky Fan [Theorem 2, Math. Z. 112 (1969), 234-240] for continuous condensing random maps and nonexpansive random maps defined on a closed convex bounded subset in a separable Hilbert space. In this paper, we prove that it is still true for (more general) continuous 1-set-contractiv...

We present existence of common random fixed point as random best approximation results for non-commuting random operators. These results improve, extend and generalize some existing known results in the literature.

We provide some new Caratheodory-type selection theorems. i.e.. selections for correspondences of two variables which are continuous with respect to one variable and measurable with respect to the other. These results generalize simultaneously Michael’s [2l] continuous selection theorem for lower-semicontinuous correspondences as well as a Caratheodory-type selection theorem of Fryszkowski [IO]...

Some random versions of deterministic fixed point theorems for condensing and nonexpansive operators are obtained.

The study of random fixed points has been an active area of contemporary research in mathematics. Some of the recent works in this field are noted in [1, 2, 3, 11]. In particular, random iteration schemes leading to random fixed points were introduced in [3]. After that, random iterations for finding solutions of random operator equations and fixed points of random operators have been discussed...

We prove some general random coincidence point theorems. Our results unify and extend several known, as well as some new, random coincidence point and random fixed point theorems.