Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry II

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 March 2025 | Viewed by 2337

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Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Interests: numerical analysis; iterative methods in Banach spaces; semilocal and local convergence; computational efficiency
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Special Issue Information

Dear Colleagues,

Recently, fixed-point theory (with topological fixed-point theory, metric fixed-point theory, and discrete fixed-point theory), geometry of Banach spaces, and symmetry have become very important and powerful tools to study nonlinear analysis and applications, especially nonlinear operator theory and applications, equilibrium problems and applications, variational inequality problems and applications, complementarity problems and applications, saddle point theory and applications, differential and integral equations and applications, optimization problems and applications, approximation theory and applications, numerical analysis and applications, the stability of functional equations, game theory and applications, programming problems and applications, engineering, topology, economics, geometry, inequality problems, and many others.

The aim of this Special Issue of Symmetry is to enhance the new development of fixed-point theory, related nonlinear problems, the geometry of Banach spaces, and symmetry with applications. Our Guest Editor will accept high-quality papers containing original results and survey articles of exceptional merit.

Due to the great success of our Special Issue "Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry", we decided to set up a second volume. We invite you to read the Special Issue at https://www.mdpi.com/journal/symmetry/special_issues/Nonlinear_Analysis_Applications_Geometry_Banach_Spaces_Symmetry

Prof. Dr. Eulalia Martínez Molada
Guest Editor

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Keywords

  • fixed-point theory and applications
  • best proximity point theory and applications
  • nonlinear operator theory and applications
  • generalized contractive mappings
  • equilibrium problems and applications
  • variational inequality problems and applications
  • optimization problems and applications
  • game theory and applications
  • numerical algorithms for nonlinear problems
  • well-posedness in fixed-point theory
  • stability of functional equations related to fixed-point theory
  • differential and integral equations
  • geometry of banach spaces
  • symmetry

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Published Papers (1 paper)

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Research

17 pages, 787 KiB  
Article
Semilocal Convergence of a Multi-Step Parametric Family of Iterative Methods
by Eva G. Villalba, Eulalia Martínez and Paula Triguero-Navarro
Symmetry 2023, 15(2), 536; https://doi.org/10.3390/sym15020536 - 17 Feb 2023
Viewed by 1687
Abstract
In this paper, we deal with a new family of iterative methods for approximating the solution of nonlinear systems for non-differentiable operators. The novelty of this family is that it is a m-step generalization of the Steffensen-type method by updating the divided [...] Read more.
In this paper, we deal with a new family of iterative methods for approximating the solution of nonlinear systems for non-differentiable operators. The novelty of this family is that it is a m-step generalization of the Steffensen-type method by updating the divided difference operator in the first two steps but not in the following ones. This procedure allows us to increase both the order of convergence and the efficiency index with respect to that obtained in the family that updates divided differences only in the first step. We perform a semilocal convergence study that allows us to fix the convergence domain and uniqueness for real applied problems, where the existence of a solution is not known a priori. After this study, some numerical tests are developed to apply the semilocal convergence theoretical results obtained. Finally, mediating the dynamic planes generated by the different numerical methods that compose the family, we study the symmetry of the basins of attraction generated by each solution, the shape of these basins, and the convergence to each root of a polynomial function. Full article
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