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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
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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 An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
Mewomo Oluwatosin T., Oyewole Olawale K.
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
335--358
EN
In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi- ϕ -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E1 and a smooth, strictly convex and reflexive Banach space E2 . Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.
4
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
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2021
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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.
5
Content available remote An abstract nonlocal functional-differential second order evolution Cauchy problem
Bednarz A., Byszewski L.
Technical Transactions
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2018
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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].
6
Content available remote Orthogonal stability of mixed type additive-cubic functional equations in multi-Banach spaces
Murali R., Pinelas S., Raj A. A.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
106--111
EN
In this paper, we establish the Hyers-Ulam orthogonal stability of the mixed type additive-cubic functional equation in multi-Banach spaces.
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
On series whose rearrangements possess discrete sets of limit points
Wituła R., Hetmaniok E., Kaczmarek K.
Journal of Applied Analysis
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2014
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Vol. 20, nr 1
93--96
EN
Aim of this short paper is to construct in any infinite-dimensional Hilbert space a series with terms tending to zero such that some of its rearrangements possess the discrete set of limit points.
9
Strong convergence theorems for the approximation of fixed points of demicontinuous pseudocontractive mappings
Chidume C. E, Shehu Y.
Journal of Applied Analysis
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2013
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Vol. 19, nr 2
213--229
EN
In this paper, we introduce a new explicit iterative scheme for approximation of fixed points of demicontinuous pseudocontractive mappings in uniformly smooth Banach spaces and prove strong convergence of our proposed iterative scheme. Furthermore, we modify our explicit iterative scheme for approximation of zeroes of bounded demicontinuous accretive mappings in uniformly smooth Banach spaces. Our result improves, extends and unifies most of the results that have been proved for this class of mappings.
10
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
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2012
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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.
11
Set-valued variational-like inclusions with H -eta-accretive operators in Banach spaces
Ahmad R.
Journal of Applied Analysis
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2011
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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.
12
Content available remote Integrodifferential evolution nonlocal problem for the first order equation
Byszewski L., Winiarska T.
Czasopismo Techniczne. Nauki Podstawowe
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2011
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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.
13
Content available remote The nonlocal Darboux problem on the unbounded region in Banach spaces
Majcher P.
Demonstratio Mathematica
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2008
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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.
14
Content available remote Chaotyczne liniowe układy dynamiczne : teoria i zastosowanie
Banasiak J.
Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
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2005
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[Z] 41
51-79
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