Józef Banaś
YOU?
Author Swipe
View article: Infinite Systems of Differential and Integral Equations: Current State and Some Open Problems
Infinite Systems of Differential and Integral Equations: Current State and Some Open Problems Open
This paper presents some topics of the theory of infinite systems of differential and integral equations. Our considerations focus on showing the symmetries that can be encountered in the theory of nonlinear differential and integral equat…
View article: Fixed point theory in RWC–Banach algebras
Fixed point theory in RWC–Banach algebras Open
In this paper, we prove some fixed point results for the sum and the product of nonlinear continuous operators acting on an RWC–Banach algebra. Our result is formulated in terms of topological conditions on the operators. An illustrative e…
View article: On solutions vanishing at infinity of infinite systems of quadratic Urysohn integral equations
On solutions vanishing at infinity of infinite systems of quadratic Urysohn integral equations Open
The paper is devoted to present a result on the existence of solutions of an infinite system of quadratic integral equations of the Urysohn type considered on the real half-axis. Our investigations are conducted in the Banach space consist…
View article: Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations
Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations Open
In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are cont…
View article: On the smoothness of normed spaces
On the smoothness of normed spaces Open
The aim of the paper is to discuss and clarify some concepts of the geometric theory of normed spaces. We mainly intend to present recent results concerning the concept of smoothness of normed spaces in connection with the concepts of the …
View article: A generalized Caputo-type fractional-order neuron model under the electromagnetic field
A generalized Caputo-type fractional-order neuron model under the electromagnetic field Open
This article considers a fractional-order neuron model under an electromagnetic field in terms of generalized Caputo fractional derivatives. The motivation for incorporating fractional derivatives in the previously proposed integer-order n…
View article: ON SOLUTIONS OF INFINITE SYSTEMS OF INTEGRAL EQUATIONS COORDINATEWISE CONVERGING AT INFINITY
ON SOLUTIONS OF INFINITE SYSTEMS OF INTEGRAL EQUATIONS COORDINATEWISE CONVERGING AT INFINITY Open
In the paper we are going to prove the existence of solutions of an infinite system of nonlinear quadratic integral equations of Volterra-Hammerstein type. Those solutions are continuous and bounded functions defined on the real half-axis…
View article: The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space
The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space Open
The aim of the paper is to introduce the Banach space consisting of real functions defined on a locally compact and countable at infinity metric space and having increments tempered by a modulus of continuity. We are going to provide a con…
View article: Solvability of an infinite system of integral equations on the real half-axis
Solvability of an infinite system of integral equations on the real half-axis Open
The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of t…
View article: Fixed point theorems in WC-Banach algebras and their applications to infinite systems of integral equations
Fixed point theorems in WC-Banach algebras and their applications to infinite systems of integral equations Open
The paper is devoted to prove a few fixed point theorems for operators acting in WC-Banach algebras and satisfying some conditions expressed in terms of a generalized Lipschitz continuity and measures of weak noncompactness. Moreover, the …
View article: Generic property of tonelli's method for ordinary differential equations
Generic property of tonelli's method for ordinary differential equations Open
In the theory of ordinary differential equations there are many methods allowing to obtain solutions of the considered equations, provided such solutions do exist.
View article: On a measure of noncompactness in the space of regulated functions and its applications
On a measure of noncompactness in the space of regulated functions and its applications Open
In this paper we formulate a criterion for relative compactness in the space of functions regulated on a bounded and closed interval. We prove that the mentioned criterion is equivalent to a known criterion obtained earlier by D. Fraňkova,…
View article: Solutions of a quadratic Volterra–Stieltjes integral equation in the class of functions converging at infinity
Solutions of a quadratic Volterra–Stieltjes integral equation in the class of functions converging at infinity Open
The paper deals with the study of the existence of solutions of a quadratic integral equation of Volterra–Stieltjes type. We are looking for solutions in the class of real functions continuous and bounded on the real half-axis $\mathbb{R}_…
View article: Existence of solutions for infinite systems of differential equations in spaces of tempered sequences
Existence of solutions for infinite systems of differential equations in spaces of tempered sequences Open
The aim of this article is to study the existence of solutions for infinite systems of differential equations. We look for solutions in Banach tempered sequence spaces, using techniques associated with measures of noncompactness, and resul…
View article: On an elementary inequality and its application in the theory of integral equations
On an elementary inequality and its application in the theory of integral equations Open
An elementary inequality is proved and some special cases of that inequality are discussed.Moreover, the usefulness of that inequality in the theory of some classes of nonlinear integral equations is shown.
View article: On Regulated Functions
On Regulated Functions Open
The main purpose of this review article is to present the concept of a regulated function and to indicate the connection of the class of regulated functions with other significant classes of functions.In particular, we give a characterizat…
View article: Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity
Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity Open
The paper is devoted to the study of the solvability of a nonlinear Volterra–Stieltjes integral equation in the class of real functions defined, bounded and continuous on the real half-axis $\mathbb{R}_+$ and having finite limits at infini…
View article: On an elementary inequality and its application in the theory of integral equations
On an elementary inequality and its application in the theory of integral equations Open
An elementary inequality is proved and some special cases of that inequality are discussed.Moreover, the usefulness of that inequality in the theory of some classes of nonlinear integral equations is shown.