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1
Content available remote Computation of solution of integral equations via fixed point results
Alqudah Manar A., Garodia Chanchal, Uddin Izhar, Nieto Juan J.
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
772--785
EN
The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.
2
Content available remote Homotopy approach for solving two-dimensional integral equations of the second kind
Hetmaniok E., Nowak I., Słota D., Zielonka A.
Computer Assisted Methods in Engineering and Science
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2016
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Vol. 23, no. 1
19--41
EN
In this paper, the two-dimensional linear and nonlinear integral equations of the second kind is analyzed. The homotopy analysis method (HAM) is used for determining the solution of the investigated equation. In this method, a solution is sought in the series form. It is shown that if this series is convergent, its sum gives the solution of the considered equation. The sufficient condition for the convergence of the series is also presented. Additionally, the error of approximate solution, obtained as partial sum of the series, is estimated. Application of the HAM is illustrated by examples.
3
Content available On the solutions of a class of nonlinear functional integral quations in space C [0,a]
Özdemir İ., Çakan Ü.
Journal of Mathematics and Applications
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2015
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Vol. 38
105--114
EN
The principal aim of this paper is to give sufficient conditions for solvability of a class of some nonlinear functional integral equations in the space of continuous functions defined on interval [0,a]. The main tool used in our study is associated with the technique of measures of noncompactness. We give also some examples satisfying the conditions of our main theorem but not satisfying the conditions in [8].
4
Content available remote The radial solution of the heat equation in the cylindrical ring
Koroński J.
Fasciculi Mathematici
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2010
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Nr 43
69-83
EN
The subject of the paper is the construction of a solution to the parabolic problem for the cylindrical ring with initial condition of Cauchy type and boundary conditions of Dirichlet type. To construct the radial solution we do not use the Bessel functions but we apply the convenient Green function, heat potentials and Banach fixed point theorem.
5
Content available remote Linear and nonlinear boundary value problems for polyharmonic equations
Bujakiewicz-Korońska R., Koroński J.
Fasciculi Mathematici
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2007
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Nr 38
5-15
EN
Boundary value problems for linear and nonlinear polyharmonic equations are studied in this paper. The theorems on uniqueness and existence of solutions for certain class of iterated elliptic equations of In order are proved.
6
Content available remote On the nonexistence of positive solution of some nonlinear integral equation
Long N. T., Ruy D. V.
Demonstratio Mathematica
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2003
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Vol. 36, nr 2
393--404
7
Content available remote A semilinear wave equation associated with a nonlinear integral equation
Long N. T., Thuyet T. M.
Demonstratio Mathematica
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2003
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Vol. 36, nr 4
915--938
8
Content available remote On the nonexistence of positive solution of a nonlinear integral equation
Long N., Binh D.
Demonstratio Mathematica
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2001
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Vol. 34, nr 4
837-845
9
Content available remote On the nonexistence of positive solution of Laplace equation in half-space Rn with a nonlinear Neumann boundary condition
Binh D. T. T., Long N. T.
Demonstratio Mathematica
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2000
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Vol. 33, nr 2
365-372
10
Content available remote Positive solutions of a nonlinear integral equation from biomathematics
Trif T.
Demonstratio Mathematica
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1999
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Vol. 32, nr 1
129-138
EN
The aim of the present paper is to investigate the existence of positive continuous solutions of the nonlinear integral equation x(t) = St-r f(s, x(s))ds, arising in infectious diseases. We give sufficient conditions ensuring the existence of positive periodic continuous solutions of this equation, provided that f is a continuous function periodic in the first argument. We also study the existence of positive continuous solutions of the initial value problem for the considered equation.
11
Content available remote Common fixed point theorems with applications to nonlinear integral equations
Pathak H., Mishra S., Kalinde A.
Demonstratio Mathematica
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1999
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Vol. 32, nr 3
547-564
EN
Various definitions of compatible maps are characterized and compared in terms of continuity of maps, fixed points and certain limits. Common fixed point theorems for a new class of compatible maps on complete metric spaces are proved. Subsequently, the main result is applied to prove the existence of solutions of two systems of nonlinear integral equation.
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