Tópico(s): Fixed Point Theorems Analysis
2002 - De Gruyter Open | Demonstratio Mathematica
Tópico(s): Differential Equations and Boundary Problems
2007 - De Gruyter Open | Demonstratio Mathematica
Abstract In this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions.
Tópico(s): Fixed Point Theorems Analysis
2019 - De Gruyter | International Journal of Nonlinear Sciences and Numerical Simulation
Dafang Zhao, Guoju Ye, Wei Liu, Delfim F. M. Torres,
We investigate properties of the fuzzy Henstock–Kurzweil delta integral (shortly, FHK $$\varDelta $$ -integral) on time scales, and obtain two necessary and sufficient conditions for FHK $$\varDelta $$ -integrability. The concept of uniformly FHK $$\varDelta $$ -integrability is introduced. Under this concept, we obtain a uniformly integrability convergence theorem. Finally, we prove monotone and dominated convergence theorems for the FHK $$\varDelta $$ -integral.
Tópico(s): Optimization and Variational Analysis
2018 - Springer International Publishing | Springer proceedings in mathematics & statistics
ABSTRACT A Henstock-Kurzweil type integral on a compact zero-dimensional metric space is investigated. It is compared with two Perron type integrals. It is also proved that it covers the Lebesgue integral.
Tópico(s): Fixed Point Theorems Analysis
2011 - De Gruyter | Tatra Mountains Mathematical Publications
We develop the theory of Henstock–Kurzweil type integral of functions with respect to metric distributions in the framework of metric spaces. In the setting of metric currents (as originated by E. De Giorgi, L. Ambrosio and B. Kirchheim) we apply the new integral to study a generalization of the Stokes theorem.
Tópico(s): Geometric Analysis and Curvature Flows
2012 - Elsevier BV | Journal of Mathematical Analysis and Applications
Abstract In this study, the basic theory of the sequential Henstock-Kurzweil delta integral on time scales will be discussed. First, we give the notion and the elementary properties of this integral; then we show the equivalence of the Henstock-Kurzweil delta integral and the sequential Henstock-Kurzweil delta integral on time scales. In addition, we consider the Cauchy criterion and the Fundamental Theorems of Calculus. Finally, we prove Henstock’s lemma and give some convergence theorems. As an ...
Tópico(s): Fractional Differential Equations Solutions
2024 - De Gruyter Open | Demonstratio Mathematica
Tópico(s): Matrix Theory and Algorithms
2005 - World Scientific | Series in real analysis
Tópico(s): Matrix Theory and Algorithms
2005 - World Scientific | Series in real analysis
Tópico(s): Algebraic and Geometric Analysis
2004 - World Scientific | Series in real analysis
Tópico(s): Algebraic and Geometric Analysis
2011 - World Scientific | Series in real analysis
Tópico(s): Holomorphic and Operator Theory
2011 - World Scientific | Series in real analysis
Tópico(s): advanced mathematical theories
2011 - World Scientific | Series in real analysis
Tópico(s): Algebraic and Geometric Analysis
2011 - World Scientific | Series in real analysis
... a Banach space. The results are obtained using Henstock-Kurzweil-Pettis integrals and De Blasi measure of weak noncompactness. An example is ...
Tópico(s): Stability and Controllability of Differential Equations
2022 - Springer International Publishing | Lecture notes in networks and systems
Tópico(s): Numerical methods in inverse problems
2020 - Société Mathématique de France | Bulletin de la Société mathématique de France
Tópico(s): Approximation Theory and Sequence Spaces
2011 - World Scientific | Series in real analysis
Salvador Sánchez-Perales, Jesús F. Tenorio,
We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.
Tópico(s): Mathematical functions and polynomials
2014 - Unión Matemática Argentina | Revista de la Unión Matemática Argentina
Let L be the one-dimensional Schrodinger operator defined by Ly=−y′′+qy. We investigate the existence of a solution to the initial value problem for the differential equation (L−λ)y=g, when q and g are Henstock–Kurzweil integrable functions on [a,b]. Results presented in this article are generalizations of classical results for the Lebesgue integral.
Tópico(s): Numerical methods for differential equations
2017 - Unión Matemática Argentina | Revista de la Unión Matemática Argentina
M. Guadalupe Morales, Juan H. Arredondo, Francisco J. Mendoza-Torres,
In this paper the Fourier transform is studied using the Henstock–Kurzweil integral on R. We obtain that the classical Fourier transform Fp:Lp(R)→Lq(R), 1/p+1/q=1 and 1<p≤2, is represented by the integral on a subspace of Lp(R), which strictly contains L1(R)∩Lp(R). Moreover, for any function f in that subspace, Fp(f) obeys a generalized Riemann–Lebesgue lemma.
Tópico(s): Differential Equations and Boundary Problems
2016 - Unión Matemática Argentina | Revista de la Unión Matemática Argentina
Juan H. Arredondo, Alfredo Reyes,
We use the Henstock-Kurzweil integral and interpolation theory to extend the Fourier cosine transform operator, broadening some classical properties such as the Riemann-Lebesgue lemma.Furthermore, we show that a qualitative difference between the cosine and sine transform is preserved on differentiable functions.
Tópico(s): Digital Filter Design and Implementation
2021 - Unión Matemática Argentina | Revista de la Unión Matemática Argentina
Tat'yana Aleksandrovna Sworowska,
The approximate symmetric Henstock-Kurzweil integral is shown as solving the problem of the recovery of a function from its trigonometric integral. This being so, we generalize Offord's theorem, which is an analogue of de la Vallee Poussin's theorem for trigonometric series. A new condition for a function to be representable by a ...
Tópico(s): Mathematical functions and polynomials
2010 - IOP Publishing | Sbornik Mathematics
Paul Musial, В. А. Скворцов, Piotr Sworowski, Francesco Tulone,
... introduced by Musial and Sagher to characterize their Henstock–Kurzweil-type integral, the HKr-integral. We show that these two classes coincide and thereby we obtain a new descriptive characterization of the class of HKr-integrable functions. We then compare the HKr-integral with Burkill's CP-integral and obtain a de la Vallée Poussin-type theorem for the HKr- ...
Tópico(s): Mathematical functions and polynomials
2024 - Elsevier BV | Journal of Mathematical Analysis and Applications
Jaroslav Kurzweil, Jifi Jarnik,
Tópico(s): Optimization and Variational Analysis
1997 - Brussels Palace of the Academies | Bulletin de la Classe des sciences
Lei Yu, J.P. Barbot, D. Benmerzouk, Driss Boutat, Thierry Floquet, G. Zheng,
... Genuinely) behaviors of switched dynamical systems. Firstly, the Henstock-Kurzweil integral is recalled in order to set up the ...
Tópico(s): Control and Dynamics of Mobile Robots
2011 - Springer Science+Business Media | Lecture notes in control and information sciences
... to the fundamental theorem of calculus for the Henstock-Kurzweil integral, we generalize existing results on increasing differences and ...
Tópico(s): Game Theory and Applications
2007 - De Gruyter | The B E Journal of Theoretical Economics
... in the linear case, are equivalent to nonlinear integrals of Henstock-Kurzweil type. In this note, it is also shown that a nonlinear measure is nothing but a linear integral of a kernel function.
Tópico(s): Fractional Differential Equations Solutions
1988 - Elsevier BV | North-Holland mathematics studies
Guoju Ye, Mingxia Zhang, Wei Liu, Dafang Zhao,
... differential equation with Neumann boundary value problem via Henstock-Kurzweil-Stieltjes integrals.The existence of solutions is derived from Schauder' ...
Tópico(s): Differential Equations and Numerical Methods
2019 - Unión Matemática Argentina | Revista de la Unión Matemática Argentina
... In the next section we formalize that the Henstock-Kurzweil integral is linear. In the last section, we verified ...
Tópico(s): Polynomial and algebraic computation
2017 - De Gruyter Open | Formalized Mathematics
Extension of Denjoy–Perron–Henstock–Kurzweil integral has been done by replacing the derivative with the approximate derivative or the distributional derivative. However even in these integrals, ...
Tópico(s): Stochastic processes and financial applications
2020 - Springer International Publishing | Springer proceedings in mathematics & statistics