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  1. 11 Journal of Mathematics and Applications
  2. 7 Commentationes Mathematicae
  3. 7 Discussiones Mathematicae, Differential Inclusions, Control and Optimization
  4. 5 Demonstratio Mathematica
  5. 4 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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  1. 1 2023
  2. 2 2022
  3. 1 2020
  4. 5 2019
  5. 4 2018
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  1. 6 Sikorska-Nowak A.
  2. 3 Kubiaczyk I.
  3. 3 Olszowy L.
  4. 2 Benchohra M.
  5. 2 Caballero J.
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1
Content available Solvability of functional quadratic integral equations with perturbation
100%
Metwali M. A. M.
Opuscula Mathematica
|
2013
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tom Vol. 33, no. 4
725--739
EN
We study the existence of solutions of the functional quadratic integral equation with a perturbation term in the space of Lebesgue integrable functions on an unbounded interval by using the Krasnoselskii fixed point theory and the measure of weak noncompactness.
2
On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval
100%
Olszowy L.
Commentationes Mathematicae
|
2008
|
tom 48
|
nr 1
EN
We show that \(\omega_0 (X) = \lim_{T\to\infty} \lim_{\varepsilon\to 0} \omega^T (X, \varepsilon)\) is a measure of noncompactness defined on some subsets of the space \(C(\mathbb{R}^+) = \{x\colon \mathbb{R}^+ \to \mathbb{R},\ x\ \text{continuous}\}\) furnished with the distance defined by the family of seminorms \(|x|_n\). Moreover, using a technique associated with the measures of noncompactness, we prove the existence of solutions of a quadratic Urysohn integral equation on an unbounded interval. This measure allows to obtain theorems on the existence of solutions of a integral equations on an unbounded interval under a weaker assumptions then the assumptions of theorems obtained by applying two-component measures of noncompactness.
3
Content available remote The Asymptotic Stability of the Functional-Integral Equation in Banach Spaces
100%
Kubiaczyk I. , Roszak M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2004
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tom Vol. 44, nr 2
271-277
4
Content available remote Measures of noncompactness related to monotonicity
100%
Banaś J. , Olszowy L.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2001
|
tom [Z] 41
13-23
EN
We investigate measures of noncompactness related to the monotonicity of functions. Several properties of these measures of non-compactness are derived. Particularly we give the estimates of these measures with help of the Hausdorff distance from the family of nondecreasing or nonincreasing functions. Such a result indicates some connections with approximation theory.
5
Analyzing the existence of solution of a fractional order integral equation: A fixed point approach
100%
Saha D. , Sen M. , Roy S.
Journal of Applied Analysis
|
2022
|
tom Vol. 28, nr 2
199--210
EN
This paper signifies the beauty of fixed point theory in the context of attaining the sufficient condition for the existence of the solution of a non-linear functional-integral equation in an unbounded interval. Here a non-linear integral equation (NLIE) involving a fractional operator is taken in the form of an operator equation. Utilizing the perception of measure of noncompactness (MNC) along with certain relevant assumptions, it is proved that the operator equation satisfies the Darbo condition for the product of operators in a Banach algebra. Finally, the result obtained is verified by the assistance of the numerical example.
6
Content available remote An existence theorem for solutions of an integro-differential equation in Banach spaces
100%
Dutkiewicz A.
Demonstratio Mathematica
|
2012
|
tom Vol. 45, nr 4
895-899
EN
The paper contains an existence theorem for local solutions of an initial value problem for a nonlinear integro-differential equation in Banach spaces. The assumptions and proofs are expressed in terms of measures of noncompactness.
7
Content available remote On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval
100%
Olszowy L.
Commentationes Mathematicae
|
2008
|
tom Vol. 48, [Z] 1
103-112
EN
We show that [formula] is a measure of noncompactness defined on some subsets of the space C(R+) = {x : R+ !R, x continuous} furnished with the distance defined by the family of seminorms |x|n. Moreover, using a technique associated with the measures of noncompactness, we prove the existence of solutions of a quadratic Urysohn integral equation on an unbounded interval. This measure allows to obtain theorems on the existence of solutions of a integral equations on an unbounded interval under a weaker assumptions then the assumptions of theorems obtained by applying two-component measures of noncompactness.
8
Content available remote Integrable solutions for quadratic Hammerstein and quadratic Urysohn functional integral equations
100%
El-Sayed A. M. A. , Hashem H. H. G.
Commentationes Mathematicae
|
2008
|
tom Vol. 48, [Z] 2
199-207
EN
The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equation have been studied in [3], [6], [7] and [9]. Here We are concerning with the existence of L1 positive monotonic solutions for the quadratic Hammerstein and quadratic Urysohn functional integral equations.
9
Content available remote Second order evolution differential functional equations with infinite delay
100%
Człapiński T. , Karpowicz A.
Commentationes Mathematicae
|
2018
|
tom Vol. 58, No. 1/2
93--104
EN
We consider a second order semilinear functional evolution equation with infinite delay in a Banach space. We prove the existence of mild solutions for this equation using the measure of noncompactness technique and the Schauder fixed point theorem.
10
Content available remote On nondecreasing solutions of cubic integral equations of Urysohn type
100%
Caballero J. , O’regan D. , Sadarangani K.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2004
|
tom Vol. 44, nr 1
39--54
EN
Using a technique associated with measures of noncompactness we prove the existence of nondecreasing solutions to cubic integral equations of Urysohn type in C[0,1].
11
Content available Existence of solutions of some quadratic integral equations
88%
Anichini G. , Conti G.
Opuscula Mathematica
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2008
|
tom Vol. 28, no. 4
433-440
EN
In this paper we study the existence of continuous solutions of quadratic integral equations. The theory of quadratic integral equations has many useful applications in mathematical physics, economics, biology, as well as in describing real world problems. The main tool used in our investigations is a fixed point result for the multivalued solution's map with acyclic values.
12
Content available remote On the existence of nondecreasing solutions of an integral equation
88%
Caballero J. , Lopez B. , Rocha J. , Sadarangani K.
Journal of Mathematics and Applications
|
2006
|
tom Vol. 28
13-24
EN
Using a technique associated with measures of noncompactness we prove the existence of nondecreasing solutions for an integral equation in C[O, 1].
13
Content available remote Existence of solutions of the dynamic Cauchy problem in Banach spaces
88%
Cichoń M. , Kubiaczyk I. , Sikorska-Nowak A. , Yantir A.
Demonstratio Mathematica
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2012
|
tom Vol. 45, nr 3
561-573
EN
In this paper we obtain the existence of solutions and Carathéodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales (…), where f is continuous or f satisfies Carathéodory conditions and some conditions expressed in terms of measures of noncompactness. The Mönch fixed point theorem is used to prove the main result, which extends these obtained for real valued functions.
14
Content available Essential norm estimates for multilinear singular and fractional integrals
88%
Meskhi A.
Commentationes Mathematicae
|
2019
|
tom 59
|
nr 1-2
EN
We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no \((m+1)\)-tuple of weights \((v,w_1, \dots, w_m)\) for which these operators are compact from \(L^{p_1}_{w_1} \times \dots \times L^{p_m}_{w_m}\) to \(L^q_v\).
15
Content available Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals
88%
Sikorska-Nowak A.
Commentationes Mathematicae
|
2007
|
tom 47
|
nr 2
EN
We prove an existence theorems for the nonlinear integral equation \[ x(t) = f (t) + \int_{0}^a k_1 (t, s)x(s)ds + \int_{0}^a k_2(t, s)g(s, x(s))ds,\quad t \in I_a = [0, a], a \in \mathbb{R} _+, \] where \(f, g, x\) are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.
16
Content available remote Existance of solutions of nonlinear integral equations and Henstock-Kurzweil integrals
88%
Sikorska-Nowak A.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2007
|
tom Vol. 47, [Z] 2
227-238
EN
We prove an existence theorems for the nonlinear integral equation... [formuła matematyczna]... where f, g, x are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.
17
Content available On the Picard problem for hyperbolic differential equations in Banach spaces
88%
Sadowski A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2003
|
tom 23
|
nr 1
31-37
EN
B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation $z_{xy} = f(x,y,z,z_{xy})$ on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation $z_{xy} = f(x,y,z,z_x,z_{xy})$ using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].
18
Content available Asymptotic behaviour of solutions of difference equations in Banach spaces
88%
Kisiołek A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2008
|
tom 28
|
nr 1
5-13
EN
In this paper we consider the first order difference equation in a Banach space $Δx_{n} = ∑_{i=0}^∞ a^{i}_{n} f(x_{n+i})$. We show that this equation has a solution asymptotically equal to a. As an application of our result we study the difference equation $Δx_{n} = ∑_{i=0}^∞ a^i_{n}g(x_{n+i}) + ∑_{i=0}^∞ b^{i}_{n}h(x_{n+i}) + y_{n}$ and give conditions when this equation has solutions. In this note we extend the results from [8,9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.
19
Content available Monotonic solutions for quadratic integral equations
88%
Cichoń M. , Metwali M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2011
|
tom 31
|
nr 2
157-171
EN
Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.
20
Content available remote On the structure of solution set of an integro-differential equation in Banach spaces
75%
Roszak M.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 2
341--348
EN
In this paper we shall present two existence theorems for local solutions of an initial value problem for nonlinear integro-differential equation in a Banach space.
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