A class of -sets
David Grow (1987)
Colloquium Mathematicae
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David Grow (1987)
Colloquium Mathematicae
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Matthew Daws (2011)
Studia Mathematica
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Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say . In this paper, we investigate properties of . We present a short proof that can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens...
M. Kostić (2021)
Archivum Mathematicum
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In this paper, we analyze multi-dimensional quasi-asymptotically -almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl -almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically -almost periodic functions and reconsider the notion of semi--periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide...
Marco Kostić, Vipin Kumar (2022)
Archivum Mathematicum
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In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely -almost periodic functions in slowly oscillating functions in and further analyze the recently introduced class of quasi-asymptotically -almost periodic...
Katusi Fukuyama (2001)
Colloquium Mathematicae
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By the method of Rio [10], for a locally square integrable periodic function f, we prove for almost every x and t > 0.
H. S. Mustafayev (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let A be a complex, commutative Banach algebra and let be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space is scattered (i.e., has no nonempty perfect subset). (b) Weakly almost periodic...
Yongxiang Li, He Yang (2011)
Annales Polonici Mathematici
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The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation , where is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].
Andrzej Krupa (2003)
Studia Mathematica
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We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on . The support of the density coincides with the spectrum of the operator in .
Shangquan Bu (2013)
Studia Mathematica
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Using known results on operator-valued Fourier multipliers on vector-valued function spaces, we give necessary or sufficient conditions for the well-posedness of the second order degenerate equations (P₂): d/dt (Mu’)(t) = Au(t) + f(t) (0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), (Mu’)(0) = (Mu’)(2π), in Lebesgue-Bochner spaces , periodic Besov spaces and periodic Triebel-Lizorkin spaces , where A and M are closed operators in a Banach space X satisfying D(A) ⊂ D(M)....
Weidong Gao, Yuanlin Li, Pingping Zhao, Jujuan Zhuang (2016)
Colloquium Mathematicae
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Let G be an additive finite abelian group. For every positive integer ℓ, let be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine for certain finite groups, including cyclic groups, the groups and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum...
Viktor Harangi (2011)
Fundamenta Mathematicae
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Let be arbitrary nonzero real numbers. An -decomposition of a function f:ℝ → ℝ is a sum where is an -periodic function. Such a decomposition is not unique because there are several solutions of the equation with -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the -decomposition is essentially unique. We characterize those periods for which essential...
Robert Krawczyk (2014)
Banach Center Publications
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In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system , where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.
Yongkun Li, Changzhao Li, Juan Zhang (2010)
Annales Polonici Mathematici
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By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), , j ∈ ℤ, ⎨ ⎩, where is a nonsingular matrix with continuous real-valued entries.
Imene Soulahia, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)
Commentationes Mathematicae Universitatis Carolinae
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The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for , , , and to show that this sum of mappings fits into the framework of a modification of...
Anatoli Ivanov, Sergiy Shelyag (2023)
Archivum Mathematicum
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A class of nonlinear simple form differential delay equations with a -periodic coefficient and a constant delay is considered. It is shown that for an arbitrary value of the period , for some , there is an equation in the class such that it possesses an asymptotically stable -period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The...
Yongxiang Li, Ailan Liu (2018)
Mathematica Bohemica
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This paper deals with the existence of positive -periodic solutions for the neutral functional differential equation with multiple delays The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of and the coefficient function , and the nonlinearity . Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.
Alejandro Illanes (2006)
Colloquium Mathematicae
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For a metric continuum X, let C(X) (resp., ) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and be the induced functions given by and . In this paper, we prove that: • If is almost continuous, then f is continuous. • If C(f) is almost continuous and X is locally connected, then f is continuous. • If X is not locally connected, then there exists an almost continuous function f: X → [0,1]...
Saak S. Gabriyelyan (2013)
Fundamenta Mathematicae
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Let (G,τ) be a Hausdorff Abelian topological group. It is called an s-group (resp. a bs-group) if there is a set S of sequences in G such that τ is the finest Hausdorff (resp. precompact) group topology on G in which every sequence of S converges to zero. Characterizations of Abelian s- and bs-groups are given. If (G,τ) is a maximally almost periodic (MAP) Abelian s-group, then its Pontryagin dual group is a dense -closed subgroup of the compact group , where is the group G with...
Lars Omlor, Michael Leinert (2010)
Banach Center Publications
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If G is a locally compact group with a compact invariant neighbourhood of the identity e, the following property (*) holds: For every continuous positive definite function h≥ 0 with compact support there is a constant such that for every continuous positive definite g≥0, where is left translation by x. In [L], property (*) was stated, but the above inequality was proved for special h only. That “for one h” implies “for all h” seemed obvious, but turned out not to be obvious at...
Lukas Spiegelhofer (2014)
Acta Arithmetica
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Integer sequences of the form , where 1 < c < 2, can be locally approximated by sequences of the form ⌊nα+β⌋ in a very good way. Following this approach, we are led to an estimate of the difference , which measures the deviation of the mean value of φ on the subsequence from the expected value, by an expression involving exponential sums. As an application we prove that for 1 < c ≤ 1.42 the subsequence of the Thue-Morse sequence indexed by attains both of its values with...
W. R. Utz (1971)
Annales Polonici Mathematici
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Zhiyong Wang, Zhengya Qian (2024)
Mathematica Bohemica
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We investigate the existence of infinitely many periodic solutions for the -Laplacian Hamiltonian systems. By virtue of several auxiliary functions, we obtain a series of new super- growth and asymptotic- growth conditions. Using the minimax methods in critical point theory, some multiplicity theorems are established, which unify and generalize some known results in the literature. Meanwhile, we also present an example to illustrate our main results are new even in the case . ...
W. D. Gao, R. Thangadurai (2003)
Colloquium Mathematicae
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We study the structure of longest sequences in which have no zero-sum subsequence of length n (or less). We prove, among other results, that for and d arbitrary, or and d = 3, every sequence of c(n,d)(n-1) elements in which has no zero-sum subsequence of length n consists of c(n,d) distinct elements each appearing n-1 times, where and .
Lingbin Kong, Daqing Jiang (1998)
Annales Polonici Mathematici
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The fourth order periodic boundary value problem , 0 < t < 2π, with , i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of .
Simon Lücking (2014)
Colloquium Mathematicae
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Let G be a metrizable, compact abelian group and let Λ be a subset of its dual group Ĝ. We show that has the almost Daugavet property if and only if Λ is an infinite set, and that has the almost Daugavet property if and only if Λ is not a Λ(1) set.