Convex and Numerical Analysis Research Group • Grupo de investigación Análisis Convexo y numérico (FQM 359)

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Publications

The most outstanding publications of the members of the group since its constitution are listed below:

2022

  • Ben Amara, K., Berenguer, M. I., Jeribi, A., Approximation of the Fixed Point of the Product of Two Operators in Banach Algebras with Applications to Some Functional Equations, Mathematics, 2022, 10(22), 4179. ARTICLE

  • M. I. Berenguer, , M. Ruiz Galán, An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator, Mathematics 2022, 10 (7), 1012. https://doi.org/10.3390/math10071012 ARTICLE
2021
  • A.I. Garralda-Guillem, H. Kunze, D. La Torre, M. Ruiz Galán, A Computational Study for Solving Inverse Problems for Mixed Variational Equations on Perforated Domains, In: Recent Developments in Mathematical, Statistical and Computational Sciences, 277—287, Springer Proceedings in Mathematics & Statistics 343, Springer, Cham, 2021. ARTICLE
  • A.I. Garralda-Guillem, P. Montiel López, Numerical solution for an inverse variational problem, Optimization and Engineering 22 (2021), 2537-2552. ARTICLE
2020
  • M. Arana-Jiménez, M.I. Berenguer, D. Gámez, A.I. Garralda-Guillem, M. Ruiz Galán, A perturbed collage theorem and its application to inverse interval integral problems, Comm. Nonlinear Sci. Numer. Simul. 90 (2020), 105365 ARTICLE
  • M.I. Berenguer, D. Gámez, Projected iterations of fixed point type to solve nonlinear partial Volterra integro-differential equations, Bull. Malays. Math. Sci. Soc. 43 (2020), 4431-4442  ARTICLE
  • M. I. Berenguer, D. Gámez, A.I. Garrralda-Guillem, M. Ruiz Galán, Minimax inequalities and variational equations, In: Optimization of complex systems: theory, models, algorithms and applications, 518-525, Advances in Intelligent Systems and Computing 991, Springer, Cham, 2020. CHAPTER
  • A.I. Garralda-Guillem, H. Kunze, D. La Torre, M. Ruiz Galán, Using the generalized collage theorem for estimating unknown parameters in perturbed mixed variational equations, Comm. Nonlinear Sci. Numer. Simul. 91 (2020), 105433 ARTICLE
  • P. Montiel López, A minimax approach for inverse inequalities, Comm. Nonlinear Sci. Numer. Simul. 90 (2020), 105339 ARTICLE
2019
  • A.I. Garrralda-Guillem, M. Ruiz Galán, A minimax approach for the study of systems of variational equations and related Galerkin schemes, J. Comput. Appl. Math. 354 (2019), 103-111. ARTICLE
  • P. Montiel López, M. Ruiz Galán, Infinite programming and theorems of the alternative, Math. Meth. Appl. Sci. 42 (2019), 5769-5778. ARTICLE
  • M. Ruiz Galán, Minimax inequalities and optimization, Bol. Estad. Investig. Oper. 35 (2019), 198-214. ARTICLE
2018
  • M.I. Berenguer, D. Gámez, Numerical solving of several types of two-dimensional integral equations and estimation of error bound, Math. Meth. Appl. Sci. 41 (2018), 7351–7366. ARTICLE
  • H. Kunze, D. La Torre, M. Ruiz Galán, Using the collage method to solve inverse problems for vector-valued variational problems on a perforated domain in reflexive Banach spaces. In: Recent Advances in Mathematical and Statistical Methods, 105-114, Springer Proc. Math. Stat. 259, Springer, New York, 2018. CHAPTER
  • M. Ruiz Galán, Elementary convex techniques for equilibrium, minimax and variational problems, Optim. Lett. 12 (2018), 137–154. ARTICLE
  • M. Ruiz Galán, Minimax inequalities in the absence of topological assumptions, Minimax Theory Appl. 3 (2018), 81–90. ARTICLE
2017
  • M.I. Berenguer, D. Gámez, A computational method for solving a class of two dimensional Volterra integral equation, J. Comput. Appl. Math. 318 (2017) 403-410.ARTICLE
  • M.I. Berenguer, D. Gámez, A. J. López Linares, Solution of systems of integro-differential equations using numerical treatment of fixed point, J. Comput. Appl. Math. 315 (2017) 343–353.  ARTICLE
  • M.I. Berenguer, D. Gámez, Study on convergence and error of a numerical method for solving systems of nonlinear Fredholm-Volterra integral equations of Hammerstein type, Appl. Anal. 96 (2017), 516–527. ARTICLE
  • P. Montiel López, M. Ruiz Galán, Revisiting the Hahn–Banach theorem and nonlinear infinite programming, J. Math. Anal. Appl. 455 (2017), 1037–1050. ARTICLE
  • M. Ruiz Galán, A theorem of the alternative with an arbitrary number of inequalities and quadratic programming, J. Global Optim. 69 (2017), 427–442. ARTICLE
2016
  • M.I. Berenguer, H. Kunze, D. La Torre, M. Ruiz Galán, Galerkin method for constrained variational equations and a collage-based approach to related inverse problems, J. Comput. Appl. Math. 292 (2016), 67–75. ARTICLE
  • P. Montiel López, M. Ruiz Galán, Nonlinear programming via König’s maximum theorem, J. Optim. Theory Appl. 170 (2016), 838–852. ARTICLE
  • M. Ruiz Galán, A concave-convex Ky Fan minimax inequality, Minimax Theory Appl. 1 (2016), 111–124. ARTICLE
  • M. Ruiz Galán, A sharp Lagrange multiplier theorem for nonlinear programs, J. Global Optim. 65 (2016), 513–530. ARTICLE
  • M. Ruiz Galán, The Gordan theorem and its implications for minimax theory, J. Nonlinear Convex Anal. 17 (2016), 2385–2405. ARTICLE
2015
  • M.I. Berenguer, H. Kunze, D. La Torre, M. Ruiz Galán, Galerkin schemes and inverse boundary value problems in reflexive Banach spaces, J. Comput. Appl. Math. 275 (2015), 100–112. ARTICLE
  • M.I. Berenguer, H. Kunze, D. La Torre, M. Ruiz Galán, Set-valued nonlinear Fredholm interal equations: direct and inverse problem. In: Interdisciplinary topics in applied mathematics, modeling and computational science, 65-71, Springer Proc. Math. Stat. 117, Springer, New York, 2015. CHAPTER
  • H. Kunze, D. La Torre, K. Levere, M. Ruiz Galán, Inverse problems via the “generalized collage theorem” for vector-valued Lax-Milgram-based variational problems, Math. Probl. Eng. 2015 (2015), Art. ID 764643. ARTICLE
2014
  • M.I. Berenguer, D. Gámez, A. J. López Linares, An iterative scheme for solving systems of nonlinear Fredholm integro-differential equations, Abstr. Appl. Anal. 2014 (2014), Art. ID 401541. ARTICLE
  • A.I. Garralda-Guillem, G.N. Gatica, A. Márquez, M. Ruiz Galán, A posteriori error analysis of twofold saddle point variational formulations for nonlinear boundary value problems, IMA J. Numer. Anal. 34 (2014), 326–361. ARTICLE
  • A.I. Garralda-Guillem, M. Ruiz Galán, Mixed variational formulations in locally convex spaces, J. Math. Anal. Appl. 414 (2014), 825–849. ARTICLE
  • H. Kunze, D. La Torre, F. Mendivil, M. Ruiz Galán, R. Zaki, Fractal-based methods and inverse problems for differential equations: current state of the art, Math. Probl. Eng. 2014 (2014), Art. ID 737694. ARTICLE
  • M. Ruiz Galán, An intrinsic notion of convexity for minimax, J. Convex Anal. 21 (2014), 1105–1139. ARTICLE
2013
  • I. Berenguer, D. Gámez, A. J. López Linares, Fixed point techniques and Schauder bases to approximate to solution of the first order nonlinear mixed Fredholm-Volterra integro differential equation J. Comput. Appl. Math. 252 (2013) 52–61. ARTICLE
  • M.I. Berenguer, A.I. Garralda-Guillem, M. Ruiz Galán, An approximation method for solving systems of Volterra integro-differential equations, Appl. Numer. Math. 67 (2013) 126–135. ARTICLE
  • F. Caliò, A.I. Garralda-Guillem, E. Marchetti, M. Ruiz Galán, Numerical approaches for systems of Volterra-Fredholm integral equations, Appl. Math. Comput 225 (2013), 811–821. ARTICLE
  • B. Cascales, J. Orihuela, M. Ruiz Galán, Compactness, optimality, and risk. In: Computational and analytical mathematics, 161–218, Springer Proc. Math. Stat. 50, Springer, New York, 2013. CHAPTER
2012
  • I. Berenguer, D. Gámez, A. J. López Linares, Fixed-point iterative algorithm for the linear Fredholm-Volterra integro-differential equation, J. Appl. Math. 2012 (2012), Art. ID 370894. ARTICLE
  • M.I. Berenguer, M.V. Fernández Muñoz, A.I. Garralda-Guillem, M. Ruiz Galán, A sequential approach for solving the Fredholm integro-differential equation, Appl. Numer. Math. 62 (2012), 297–304. ARTICLE
  • F. Caliò, A.I. Garralda-Guillem, E. Marchetti, M. Ruiz Galán, About some numerical approaches for mixed integral equations, Appl. Math. Comput. 219 (2012), 464–474. ARTICLE
  • D. Gámez, Analysis of the error in a numerical method used to solve nonlinear mixed Fredholm-Volterra-Hammerstein integral equation, J. Funct. Space Appl. 2012 (2012), Art. ID 242870. ARTICLE
  • J. Orihuela, M. Ruiz Galán, A coercive James’s weak compactness theorem and nonlinear variational problems, Nonlinear Anal. 75 (2012), 598–611. ARTICLE
  • J. Orihuela, M. Ruiz Galán, Lebesgue property for convex risk measures on Orlicz spaces, Math. Financ. Econ. 6 (2012), 15–35. ARTICLE
  • M. Ruiz Galán, Characterization of the solvability of generalized constrained variational equations, Abstr. Appl. Anal. 2012 (2012), Art. ID 247425. ARTICLE
2011
  • M.I. Berenguer, D. Gámez, A.I. Garralda-Guillem, M. Ruiz Galán, M.C. Serrano Pérez, Biorthogonal systems for solving Volterra integral equation systems of the second kind, J. Comput. Appl. Math. 235 (2011), 1875–1883. ARTICLE
2010
  • M.I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. C. Serrano Pérez, Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems, Abstr. Appl. Anal. 2010 (2010), Art. ID 135216. ARTICLE
  • M.I. Berenguer, A.I. Garralda-Guilllem, M. Ruiz Galán, Biorthogonal systems approximating the solution of the nonlinear Volterra integro-differential equation, Fixed Point Theory Appl. 2010 (2010), Art. ID 470149. ARTICLE
  • F. Caliò, M.V. Fernández Muñoz, E. Marchetti, Direct and iterative methods for the numerical solution of mixed integral equations, Appl. Math. Comput. 216 (2010), 3739–3746. ARTICLE
  • M. Ruiz Galán, Convex numerical radius, J. Math. Anal. Appl. 361 (2010), 481–491. ARTICLE
  • M. Ruiz Galán, Variational equations with constraints, Appl. Math. Lett. 23 (2010), 801–806. ARTICLE
2009
  • M.I. Berenguer, M.V. Fernández Muñoz, A.I. Garralda-Guillem, M. Ruiz Galán, Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation, Fixed Point Theory Appl. 2009 (2009), Art. ID 735638. ARTICLE
  • M.I. Berenguer, D. Gámez, A.I. Garralda-Guilllem, M. Ruiz Galán, M.C. Serrano Pérez, Analytical techniques for a numerical solution of the linear Volterra integral equation of the second kind, Abstr. Appl. Anal. 2009 (2009), Art. ID 149367. ARTICLE
  • D. Gámez, A.I. Garralda-Guillem, M. Ruiz Galán, High-order nonlinear initial-value problems countably determined, J. Comput. Appl. Math. 228 (2009), 77–82. ARTICLE
  • M. Ruiz Galán, A version of the Lax-Milgram theorem for locally convex spaces, J. Convex Anal. 16 (2009), 993–1002. ARTICLE
2008
  • A. Palomares, M. Pasadas, V. Ramírez, M. Ruiz Galán, A convergence result for a least-squares method using Schauder bases, Math. Comput. Simuation 77 (2008), 274–281. ARTICLE
2007
  • E. Castro, D. Gámez, A.I. Garralda-Guillem, M. Ruiz Galán, High order linear initial-value problems and Schauder bases, Appl. Math. Model. 31 (2007), 2629–2638. ARTICLE