Maria Antonia Navascues
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Maria Antonia Navascues has a total of 44 co-authors. Here are the top co-authors by number of shared publications:
- Arya Kumar Bedabrata Chand
DEPARTMENT OF MATHEMATICS, INDIAN INSTITUTE OF TECHNOLOGY MADRAS, CHENNAI, INDIA
20 shared publications - Ram Narayan Mohapatra
Department of Mathematics, University of Central Florida, Orlando, USA
9 shared publications - María Victoria Sebastián
Centro Universitario de la Defensa de Zaragoza, Academia General Militar, Zaragoza, Spain
7 shared publications - Nasim Akhtar
Department of Mathematics, Presidency University, Kolkata, India
7 shared publications - Pasupathi Rajan
DEPARTMENT OF MATHEMATICS, INDIAN INSTITUTE OF TECHNOLOGY MADRAS, CHENNAI, INDIA
7 shared publications M. V. Sebastián
Academia General Militar, Centro Universitario de la Defensa, Zaragoza, Spain
5 shared publications
Latest Publications
- 15 May 2026
- Published by Elsevier in Chaos, Solitons & Fractals
- Vol. 209
Averaged iterative algorithms and linear dynamics
- 15 May 2026
- Published by Elsevier in Chaos, Solitons & Fractals
- Vol. 209
Averaged iterative algorithms and linear dynamics
- Open Access
- 23 February 2026
- Published by MDPI AG in Fractal and Fractional
- Vol. 10 (2) , 134
Fractional Calculus of Fractal Functions on Weighted Sobolev Spaces
In this article, the -fractal interpolation function corresponding to any function f belonging to the weighted Sobolev space is defined. The convergence of sequences of -fractal interpolation functions corresponding to mappings in with respect to the uniform norm as well as the weighted Sobolev norm is discussed. It is proved that the Riemann–Liouville fractional order integral of an -fractal interpolation function of any map is also a self-referential function interpolating a specific data set. Some aspects of the convergence of the Riemann–Liouville integral of -fractal functions when the original mappings converge are also analyzed. In short, by imposing certain conditions on the base function and the scale vector of a specific iterated function system, fractal perturbations of functions from weighted Sobolev spaces are defined. It is also proved that, under suitable hypotheses, the Riemann–Liouville fractional integral of these fractal mappings on Sobolev spaces is a fractal function of the same kind.- 23 February 2026
- Published by MDPI AG in Fractal and Fractional
- Vol. 10 (2) , 134
Open AccessFractional Calculus of Fractal Functions on Weighted Sobolev Spaces
In this article, the -fractal interpolation function corresponding to any function f belonging to the weighted Sobolev space is defined. The convergence of sequences of -fractal interpolation functions corresponding to mappings in with respect to the uniform norm as well as the weighted Sobolev norm is discussed. It is proved that the Riemann–Liouville fractional order integral of an -fractal interpolation function of any map is also a self-referential function interpolating a specific data set. Some aspects of the convergence of the Riemann–Liouville integral of -fractal functions when the original mappings converge are also analyzed. In short, by imposing certain conditions on the base function and the scale vector of a specific iterated function system, fractal perturbations of functions from weighted Sobolev spaces are defined. It is also proved that, under suitable hypotheses, the Riemann–Liouville fractional integral of these fractal mappings on Sobolev spaces is a fractal function of the same kind. - 20 December 2025
- Published by Springer Nature in Numerical Algorithms
- Vol. 103 (3) , 2169-2192
Average-based iterative methods for solving nonlinear integral equations and systems of ordinary equations
- 20 December 2025
- Published by Springer Nature in Numerical Algorithms
- Vol. 103 (3) , 2169-2192
Average-based iterative methods for solving nonlinear integral equations and systems of ordinary equations
- 4 November 2025
- Published by Elsevier in Chaos, Solitons & Fractals
- Vol. 202
Coincidence, averages and fractals
- 4 November 2025
- Published by Elsevier in Chaos, Solitons & Fractals
- Vol. 202
Coincidence, averages and fractals
- 25 October 2025
- Published by Springer Nature in Rendiconti del Circolo Matematico di Palermo Series 2
- Vol. 75 (1) , 1-17
On the range of fractal interpolation functions
- 25 October 2025
- Published by Springer Nature in Rendiconti del Circolo Matematico di Palermo Series 2
- Vol. 75 (1) , 1-17
On the range of fractal interpolation functions
- Open Access
- 17 July 2025
- Published by MDPI AG in Algorithms
- Vol. 18 (7) , 439
Iterative Matrix Techniques Based on Averages
Matrices have an important role in modern engineering problems like artificial intelligence, biomedicine, machine learning, etc. The present paper proposes new algorithms to solve linear problems involving finite matrices as well as operators in infinite dimensions. It is well known that the power method to find an eigenvalue and an eigenvector of a matrix requires the existence of a dominant eigenvalue. This article proposes an iterative method to find eigenvalues of matrices without a dominant eigenvalue. This algorithm is based on a procedure involving averages of the mapping and the independent variable. The second contribution is the computation of an eigenvector associated with a known eigenvalue of linear operators or matrices. Then, a novel numerical method for solving a linear system of equations is studied. The algorithm is especially suitable for cases where the iteration matrix has a norm equal to one or the standard iterative method based on fixed point approximation converges very slowly. These procedures are applied to the resolution of Fredholm integral equations of the first kind with an arbitrary kernel by means of orthogonal polynomials, and in a particular case where the kernel is separable. Regarding the latter case, this paper studies the properties of the associated Fredholm operator.
- 17 July 2025
- Published by MDPI AG in Algorithms
- Vol. 18 (7) , 439
Open AccessIterative Matrix Techniques Based on Averages
Matrices have an important role in modern engineering problems like artificial intelligence, biomedicine, machine learning, etc. The present paper proposes new algorithms to solve linear problems involving finite matrices as well as operators in infinite dimensions. It is well known that the power method to find an eigenvalue and an eigenvector of a matrix requires the existence of a dominant eigenvalue. This article proposes an iterative method to find eigenvalues of matrices without a dominant eigenvalue. This algorithm is based on a procedure involving averages of the mapping and the independent variable. The second contribution is the computation of an eigenvector associated with a known eigenvalue of linear operators or matrices. Then, a novel numerical method for solving a linear system of equations is studied. The algorithm is especially suitable for cases where the iteration matrix has a norm equal to one or the standard iterative method based on fixed point approximation converges very slowly. These procedures are applied to the resolution of Fredholm integral equations of the first kind with an arbitrary kernel by means of orthogonal polynomials, and in a particular case where the kernel is separable. Regarding the latter case, this paper studies the properties of the associated Fredholm operator.
- 19 May 2025
- Published by Springer Nature in Arabian Journal of Mathematics
- Vol. 15 (3) , 1647-1660
New iterative methods for fixed point approximation: application to the numerical solution of Fredholm integral equations
- 19 May 2025
- Published by Springer Nature in Arabian Journal of Mathematics
- Vol. 15 (3) , 1647-1660
New iterative methods for fixed point approximation: application to the numerical solution of Fredholm integral equations
- Open Access
Hammerstein Nonlinear Integral Equations and Iterative Methods for the Computation of Common Fixed Points
In the first part of this article, a special type of Hammerstein nonlinear integral equation is studied. A theorem of the existence of solutions is given in the framework of -spaces. Afterwards, an iterative method for the resolution of this kind of equations is considered, and the convergence of this algorithm towards a solution of the equation is proved. The rest of the paper considers two modifications of the algorithm. The first one is devoted to the sought of common fixed points of a family of nearly asymptotically nonexpansive mappings. The second variant focuses on the search of common fixed points of a finite number of nonexpansive operators. The characteristics of convergence of these methods are studied in the context of uniformly convex Banach spaces. The iterative scheme is applied to approach the common solution of three nonlinear integral equations of Hammerstein type.Open AccessHammerstein Nonlinear Integral Equations and Iterative Methods for the Computation of Common Fixed Points
In the first part of this article, a special type of Hammerstein nonlinear integral equation is studied. A theorem of the existence of solutions is given in the framework of -spaces. Afterwards, an iterative method for the resolution of this kind of equations is considered, and the convergence of this algorithm towards a solution of the equation is proved. The rest of the paper considers two modifications of the algorithm. The first one is devoted to the sought of common fixed points of a family of nearly asymptotically nonexpansive mappings. The second variant focuses on the search of common fixed points of a finite number of nonexpansive operators. The characteristics of convergence of these methods are studied in the context of uniformly convex Banach spaces. The iterative scheme is applied to approach the common solution of three nonlinear integral equations of Hammerstein type. - Open Access
- 17 December 2024
- Published by MDPI AG in Fractal and Fractional
- Vol. 8 (12) , 745
An Iterative Method for the Approximation of Common Fixed Points of Two Mappings: Application to Fractal Functions
This paper proposes an iterative algorithm for the search for common fixed points of two mappings. The properties of approximation and convergence of the method are analyzed in the context of Banach spaces. In particular, this article provides sufficient conditions for the strong convergence of the sequence generated by the iterative scheme to a common fixed point of two operators. The method is illustrated with some examples of application. The procedure is used to approach a common solution of two Fredholm integral equations of the second kind. In the second part of the article, the existence of a fractal function coming from two different Read–Bajraktarević operators is proved. Afterwards, a study of the approximation of fixed points of a fractal convolution of operators is performed, in the framework of Lebesgue or Bochner spaces.
- 17 December 2024
- Published by MDPI AG in Fractal and Fractional
- Vol. 8 (12) , 745
Open AccessAn Iterative Method for the Approximation of Common Fixed Points of Two Mappings: Application to Fractal Functions
This paper proposes an iterative algorithm for the search for common fixed points of two mappings. The properties of approximation and convergence of the method are analyzed in the context of Banach spaces. In particular, this article provides sufficient conditions for the strong convergence of the sequence generated by the iterative scheme to a common fixed point of two operators. The method is illustrated with some examples of application. The procedure is used to approach a common solution of two Fredholm integral equations of the second kind. In the second part of the article, the existence of a fractal function coming from two different Read–Bajraktarević operators is proved. Afterwards, a study of the approximation of fixed points of a fractal convolution of operators is performed, in the framework of Lebesgue or Bochner spaces.
- 12 December 2024
- Published by Elsevier in Chaos, Solitons & Fractals
- Vol. 191
New algorithms for the approximation of fixed points and fractal functions
- 12 December 2024
- Published by Elsevier in Chaos, Solitons & Fractals
- Vol. 191
New algorithms for the approximation of fixed points and fractal functions