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1
Content available Measures of growth and approximation of entire harmonic functions in n-dimensional space in some Banach spaces
Kumar Devendra
Journal of Mathematics and Applications
|
2021
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Vol. 44
57--70
EN
The relationship between the classical order and type of an entire harmonic function in space Rn, n≥3, and the rate of its best harmonic polynomial approximation for some Banach spaces of functions harmonic in the ball of radius R has been studied.
2
Content available remote Some aspects of generalized Zbăganu and James constant in Banach spaces
Liu Qi, Sarfraz Muhammad, Li Yongjin
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
299--310
EN
We shall introduce a new geometric constant CZ(λ, μ, X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, CZ(λ, μ, X) is equal to 1 if and only if the norm is induced by an inner product. Next, a characterization of uniformly non-square is given, that is, X has the fixed point property. Also, a sufficient condition which implies weak normal structure is presented. Moreover, a generalized James constant J(λ, X) is also introduced. Finally, some basic properties of this new coefficient are presented.
3
Content available remote A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces
Jolaoso Lateef Olakunle
Demonstratio Mathematica
|
2021
|
Vol. 54, nr 1
527--547
EN
In this paper, we introduce a self-adaptive projection method for finding a common element in the solution set of variational inequalities (VIs) and fixed point set for relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth real Banach spaces. We prove a strong convergence result for the sequence generated by our algorithm without imposing a Lipschitz condition on the cost operator of the VIs. We also provide some numerical examples to illustrate the performance of the proposed algorithm by comparing with related methods in the literature. This result extends and improves some recent results in the literature in this direction.
4
Content available The practical feedback stabilization for evolution equations in Banach spaces
Hanen Damak
Acta Mechanica et Automatica
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2021
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Vol. 15, no. 2
58--65
EN
This paper investigates the notion of practical feedback stabilization of evolution equations satisfying some relaxed conditions in infinite-dimensional Banach spaces. Moreover, sufficient conditions are presented that guarantee practical stabilizability of uncertain systems based on Lyapunov functions. These results are applied to partial differential equations.
5
Content available remote Normal structure in modulated topological vector spaces
Kozlowski Wojciech M.
Commentationes Mathematicae
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2020
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Vol. 60, No. 1/2
1--11
EN
Following the author’s recent paper On modulated topological vector spaces and applications, Bull. Aust. Math. Soc. (2020), we discuss a notion of modulated topological vector spaces, that generalise, among others, Banach spaces and modular function spaces. The interest in modulars reflects the fact that the notions of “norm like” but “non-euclidean” (i.e., possibly without the triangle property and non-necessarily homogenous) constructs to measure a level of proximity between complex objects have been used extensively in statistics and applied in many empirical scientific projects requiring an objective differentiation between several classes of objects, efficiently applied in many modern clustering and Artificial Intelligence (AI) related computer algorithms. As an example of application, we prove some results, which extend fixed point theorems from the above mentioned paper, by moving from the setting of admissible sets to a simpler and more general setup, which covers also closed bounded sets. The theory of modulated topological vector spaces provides a very minimalistic framework, where powerful geometrical, fixed point, approximation and optimisation theorems are valid under a bare minimum of assumptions.
6
Content available remote An abstract nonlocal functional-differential second order evolution Cauchy problem
Bednarz A., Byszewski L.
Technical Transactions
|
2018
|
Vol. 115, iss. 4
139--147
EN
The aim of the paper is to prove two theorems on the existence and uniqueness of mild and classical solutions of a semilinear functional-differential evolution second order equation together with nonlocal initial conditions. The theory of strongly continuous cosine families of linear operators in a Banach space is applied. The paper is based on publications [1–12] and is a generalization of paper [7].
PL
W artykule udowodniono dwa twierdzenia o istnieniu i jednoznaczności całkowych i klasycznych rozwiązań semiliniowego funkcjonalno-różniczkowego zagadnienia ewolucyjnego Cauchy’ego rzędu drugiego z nielokalnymi warunkami początkowymi. W tym celu zastosowano teorię rodziny cosinus liniowych operatorów w przestrzeni Banacha. Artykuł bazuje na publikacjach [1–12] i jest uogólnieniem publikacji [7].
7
Approximation of entire transcendental functions of several complex variables in some Banach spaces for slow growth
Kumar D.
Journal of Applied Analysis
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2017
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Vol. 23, nr 1
9--20
EN
In the present paper, the coefficients characterizations of generalized type Tm(f; α, α) of entire transcendental functions f of several complex variables m (m ≥ 2) for slow growth have been obtained in terms of the sequence of best polynomial approximations of f in the Hardy Banach spaces Hq(Um) and in the Banach spaces Bm(p, q, λ). The presented work is the extension and refinement of the corresponding assertions made by Vakarchuk and Zhir [20-25], Gol’dberg [4] and Sheremeta [17, 18] to the multidimensional case.
8
Content available remote On Banach spaces of regulated functions
Drewnowski L.
Commentationes Mathematicae
|
2017
|
Vol 57, No. 2
153--169
EN
For a relatively compact subset S of the real line R, let R(S) denote the Banach space (under the sup norm) of all regulated scalar functions defined on S. The purpose of this paper is to study those closed subspaces of R(S) that consist of functions that are left-continuous, right-continuous, continuous, and have a (two-sided) limit at each point of some specified disjoint subsets of S. In particular, some of these spaces are represented as C(K) spaces for suitable, explicitly constructed, compact spaces K.
9
Content available remote Series representation of compact linear operators in Banach spaces
Edmunds D., Lang J.
Commentationes Mathematicae
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2016
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Vol 56, No. 1
17--27
EN
Let p∈(1,∞) and I=(0,1); suppose that T:Lp(I)→Lp(I) is a~compact linear map with trivial kernel and range dense in Lp(I). It is shown that if the Gelfand numbers of T decay sufficiently quickly, then the action of T is given by a series with calculable coefficients. The special properties of Lp(I) enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.
10
Content available remote Characterization of inclusion among Riesz−Medvedev variation spaces
Aziz W., Ereú T.
Commentationes Mathematicae
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2016
|
Vol 56, No. 2
225--237
EN
We present a characterization of inclusion among Riesz−Medvedev bounded variation spaces, i.e., we shall present necessary and sufficient conditions for the Young functions φ1 and φ2 so that RVφ1[a,b]⊂RVφ2[a,b] or RV∗φ1[a,b]⊂RV∗φ2[a,b] .
11
Content available remote Asymptotically hilbertian modular Banach spaces : examples of uncountable categoricity
Henson C. W., Raynaud Y.
Commentationes Mathematicae
|
2016
|
Vol 56, No. 1
119--144
EN
We give a criterion ensuring that the elementary class of a modular Banach space E (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of E) consists of all direct sums E⊕mH, where H is an arbitrary Hilbert space and ⊕m denotes the modular direct sum. Also, we give several families of examples in the class of Nakano direct sums of finite dimensional normed spaces that satisfy this criterion. This yields many new examples of uncountably categorical Banach spaces, in the model theory of Banach space structures.
12
Content available remote Common fixed points of a three-step iteration with errors of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense in Banach spaces
Okeke G A, Olaleru J. O.
Fasciculi Mathematici
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2014
|
Nr 52
93--115
EN
In this paper, we extend the results of Inprasit and Wattanataweekul [7] to the class of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense. We prove some strong convergence theorems for asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense using a three-step iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Our results extends, improves, unifies and generalizes the results of [13], [25] and [27].
13
Content available remote Approximation of fixed points of some classes of nonlinear mappings
Okeke G A
Fasciculi Mathematici
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2014
|
Nr 53
113--127
EN
We introduce a new class of nonlinear mappings, the class of generalized strongly successively Φ- hemicontractive mappings in the intermediate sense and prove the convergence of Mann type iterative scheme with errors to their fixed points. This class of nonlinear mappings is more general than those defined by several authors. In particular, the class of generalized strongly successively Φ- hemicontractive mappings in the intermediate sense introduced in this study is more general than the class defined by Liu et al. [Z. Liu, J. K. Kim and K. H. Kim, Convergence theorems and stability problems of the modified Ishikawa iterative sequences for strictly successively hemicontractive mappings, Bull. Korean Math. Soc. 39 (2002), No. 3, pp. 455-469].
14
Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems
Shehu Y., Oguguo O.
Journal of Applied Analysis
|
2012
|
Vol. 18, nr 1
69-95
EN
In this paper, we construct a new iterative scheme by hybrid methods to approximate a common element in the fixed points set of an infinite family of relatively quasi-nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. We give several applications of our results in a Banach space. Our results extend many known recent results in the literature.
15
Set-valued variational-like inclusions with H -eta-accretive operators in Banach spaces
Ahmad R.
Journal of Applied Analysis
|
2011
|
Vol. 17, nr 1
105-117
EN
In this work, a new class of set-valued variational-like inclusions involving H - η-accretive operators is introduced and studied. A new iterative procedure for computing approximate solutions for the class of set-valued variational-like inclusions and convergence results are established.
16
Content available remote Integrodifferential evolution nonlocal problem for the first order equation
Byszewski L., Winiarska T.
Czasopismo Techniczne. Nauki Podstawowe
|
2011
|
R. 108, z. 1-NP
15-21
EN
The aim of the paper is to prove two theorems on the existence and uniqueness of mild and classical solutions of a semilinear integrodifferential evolution nonlocal Cauchy problem for the first order equation. The method of semigroups and the Banach fixed point theorem are applied to prove the existence and uniqueness of the solutions of the problem considered.
PL
W pracy dowodzimy dwóch twierdzeń o istnieniu i jednoznaczności całkowych i klasycznych rozwiązań semiliniowego różniczkowo-całkowego ewolucyjnego nielokalnego zagadnienia Cauchy'ego dla równania rzędu pierwszego. Aby udowodnić istnienie i jednoznaczność rozwiązań rozważanego zagadnienia stosowana jest metoda półgrup i twierdzenie Banacha o punkcie stałym.
17
Content available remote A Natural Class of Sequential Banach Spaces
Talponen J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2011
|
Vol. 59, no 2
185--196
EN
We introduce and study a natural class of variable exponent ℓp spaces, which generalizes the classical spaces ℓp and c0. These spaces will typically not be rearrangement-invariant but instead they enjoy a good local control of some geometric properties. Some geometric examples are constructed by using these spaces.
18
Content available remote Essentially incomparable Banach spaces of continuous functions
Fajardo R. A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2010
|
Vol. 58, no 3
247-258
EN
We construct, under Axiom 0, a family (C(Kξ))ξ < 2(2ω) of indecomposable Banach spaces with few operators such that every operator from C(Kξ) into C(Kη) is weakly compact, for all ξ ≠ η. In particular, these spaces are pairwise essentially incomparable. Assuming no additional set-theoretic axiom, we obtain this result with size 2ω instead of 2(2ω).
19
Content available remote The nonlocal Darboux problem on the unbounded region in Banach spaces
Majcher P.
Demonstratio Mathematica
|
2008
|
Vol. 41, nr 2
389-402
EN
In this paper we study existence theorems of solutions for the hyperbolic Darboux problem of the form [..] with nonlocal boundary conditions u(x, 0) +h1(u) = g1(x),u(0,y) +h2(u)= g2(y), on the unbounded region. The functions defining nonlocal conditions satisfy the Lipschitz condition with respect to a measure of noncompactness.
20
Content available remote An arithmetic characterization of decomposition methods in Banach spaces similar to Pełczyńsk's decomposition method
Galego E. M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2004
|
Vol. 52, nr 3
273-282
EN
Inspired by Pełczyński's decomposition method in Banach spaces, we introduce the notion of Schroeder-Bernstein quadruples for Banach spaces. Then we use some Banach spaces constructed by W. T. Gowers and B. Maurey in 1997 to characterize them.
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