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1
Content available remote A new iteration method for the solution of third-order BVP via Green's function
Akgun Fatma Aydın, Rasulov Zaur
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
425--435
EN
In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.
2
Content available remote Orthogonal stability of the generalized quadratic functional equations in the sense of Rätz
Aiemsomboon Laddawan, Sintunavarat Wutiphol
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
523--530
EN
Let (X, ⊥) be an orthogonality module in the sense of Rätz over a unital Banach algebra A and Y be a real Banach module over A. In this paper, we apply the alternative fixed point theorem for proving the Hyers-Ulam stability of the orthogonally generalized k-quadratic functional equation of the form af(kx+y) + af(kx-y) = f(ax+ay) + f(ax-ay) + (2k2-2)f(ax) for some |k|>1, for all a∈A1:= {u∈A|‖u‖ = 1} and for all x,y∈X with x⊥y, where f maps from X to Y.
3
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.
4
Content available remote Approximation of additive functional equations in NA Lie C*-algebras
Wang Z., Saadati R.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
37--44
EN
In this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation [wzór], where m ≥ 2.
5
Content available remote Common fixed point and best approximation for Banach operator pairs in non-starshaped domain
Nashine H.
Demonstratio Mathematica
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2009
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Vol. 42, nr 4
797-807
EN
Common fixed point results for Banach operator pair with generalized nonexpansive mappings in non-starshaped domain of metric space have been obtained in the present work. As application, more general best approximation results in normed space have also been determined. These results extend and generalize various existing known results with the aid of Banach operator pair and without starshaped condition of domain.
6
Content available remote On Volterra-Fredholm integral equation in two variables
Pachpatte B.
Demonstratio Mathematica
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2007
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Vol. 40, nr 4
839-852
EN
The aim of this paper is to study thexistence, uniqueness and other properties of solution of a certain Volterra-Fredholm integral equation in two independent variables. The main tools employed in the analysis are based on the applications of the well known Banach fixed point theorem and the new integral inequality with explicit estimate.
7
Content available remote Iterative equations in p-normes spaces
Żołdak M.
Demonstratio Mathematica
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2006
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Vol. 39, nr 3
571-578
EN
Let X be a real p-normed, complete space and V be a nonempty closed subset of X. We consider the functional equation.
8
Content available remote Fixed-point technique in the problem of shape identification
Peterson W.
Archives of Electrical Engineering
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1999
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Vol. 48, nr 1-2
89-98
EN
A shape of an inaccessible boundary between piecewise homogeneous media of different electrical properties is identified. The method employs a dc current field excited in the region of interest by the system of auxiliary electrodes. Non-linear algebraic equations resulting from the system of Fredholm integral equations of the first kind are solved applying a fixed-point technique based on Brouwer's theorem. Because the equations are ill-posed the use of standard procedures such as Newton-Raphson, steepest descents or the method of simple iterations occured ineffective. Numerical example is illustrated for the case of a boundary between conducting and dielectric media.
PL
Przedmiotem badań jest identyfikacja kształtu niedostępnej granicy rozdzielającej przedziałami jednorodne ośrodki o różnych właściwościach elektrycznych. Metoda wykorzystuje pole prądu stałego wzbudzonego w interesującym obszarze przez układ pomocniczych elektrod liniowych. Nieliniowy układ równań algebraicznych otrzymany w wyniku numerycznego przekształcenia równań całkowych Fredholma pierwszego rodzaju został rozwiązany stosując metodę punktu stałego opartą na twierdzeniu Brouwera. Zastosowanie standardowych metod rozwiązania równań nieliniowych takich jak metoda Newtona-Raphsona lub metoda najszybszego spadku okazało się niemożliwe ze względu na złe uwarunkowanie równań. Przedstawiono przykład numeryczny dla granicy między środowiskiem przewodzącym i dielektrycznym.
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