in this work, different types of chaotic 1-manifolds which lie on the chaotic spheres or on a torus are introduced. some types of retractions of the chaotic spheres affect on the 1-chaotic systems, and other types of retractions occur to the geometric manifold but make the 1-chaotic manifold invariant. the existed retractions are discussed through new proved theorems. also we construct diffe...

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K → K be an I-asymptotically quasi-nonexpansive type mapping and I : K → K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type ma...

Throughout this paper, we denote by N, Z, Q and R the sets of all positive integers, all integers, all rational numbers and all real numbers, respectively. We put R+ = [0,∞)n and ej = (0, 0, · · · , 0, 0, (j) 1 , 0, 0, · · · , 0) ∈ R for j ∈ N with 1 ≤ j ≤ n. Let C be a subset of a Banach space E, and let T be a nonexpansive mapping on C, i.e., ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We know that T ...

We present several new results on the asymptotic behavior of firmly nonexpansive mappings in Banach spaces and in the Hubert ball. Let D be a subset of a (real) Banach space X. Recall that a mapping T: D -» X is said to be firmly nonexpansive [2, 4] if for each x and y in D, the convex function /: [0,1] -> [0, oo) defined by f{s) = \(\-s)x + sTx-((l-s)y + sTy) \ is nonincreasing. Note that T is...

Given a collection of algorithms, the Algorithm Selection (AS) problem consists in identifying which of them is the best one for solving a given problem. In this paper we show how we adapted the algorithm selector SUNNY, originally tailored for constraint solving, to deal with general AS problems. Preliminary investigations based on the AS Library benchmarks already show some promising results:...

In many computing systems, information is produced and processed by many people. Knowing how much a user trusts a source can be very useful for aggregating, filtering, and ordering of information. Furthermore, if trust is used to support decision making, it is important to have an accurate estimate of trust when it is not directly available, as well as a measure of confidence in that estimate. ...

We construct random iterative processes for weakly contractive and asymptotically nonexpansive random operators and study necessary conditions for the convergence of these processes. It is shown that they converge to the random fixed points of these operators in the setting of Banach spaces. We also proved that an implicit random iterative process converges to the common random fixed point of a...

In 1977, Baillon and Haddad proved that if the gradient of a convex and continuously differentiable function is nonexpansive, then it is actually firmly nonexpansive. This result, which has become known as the Baillon-Haddad theorem, has found many applications in optimization and numerical functional analysis. In this note, we propose short alternative proofs of this result and strengthen its ...