2 3 Se p 20 05 An intermediate value theorem for sequences with terms in a finite set
نویسندگان
چکیده
We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages {x̄n}n≥1 of sequences with terms in a given finite set {a1, ..., ar}. For every such set we completely characterize the numbers Π (”intermediate values”) with the property that the consecutive averages {x̄n} of every sequence {xn}n≥1 with terms in {a1, ..., ar} cannot increase from a value x̄k < Π to a value x̄l > Π without taking the value x̄s = Π for some s with k < s < l. (2000) Mathematics Subject Classification: 11B99, 26D15
منابع مشابه
On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings
In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...
متن کاملThe uniqueness theorem for inverse nodal problems with a chemical potential
In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.
متن کاملSOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS
In this paper, we study fuzzy calculus in two main branches differential and integral. Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating $gH$-derivative of a composite function. Two techniques namely, Leibniz's rule and integration by parts are introduced for ...
متن کامل2 2 Se p 20 05 The Number of Finite Groups Whose Element Orders is Given
For any group G, πe(G) denotes the set of orders of its elements. If Ω is a non-empty subset of N, h(Ω) stands for the number of isomorphism classes of finite groups G such that πe(G) = Ω. We put h(G) = h(πe(G)). In this paper we show that h(P GL(2, p n)) = 1 or ∞, where p = 2 α 3 β + 1 is a prime, α ≥ 0, β ≥ 0 and n ≥ 1. In particular, we show that h(P GL(2, 7)) = h(P GL(2, 3 2)) = ∞.
متن کاملRing structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کامل