Complete Metric Spaces: A Survey
DOI:
https://doi.org/10.31305/rrijm2024.v04.n02.006Keywords:
Complete metric spaces, Fixed point results, Schauder’s Theorem, Banach contraction principleAbstract
Complete metric spaces are highly important not only in mathematical theories but also in control system engineering, signal processing, machine learning, data science, etc. Completion of metric space plays a very important role in the fixed point theory. The theory of fixed points has been applied by researchers for several years in optimization problems, nonlinear analysis, dynamic system theory, control theory, signal and image processing, economics, game theory, chemical engineering, electrical engineering, etc. In this article, we present a sur- vey of such direct and indirect applications of complete metric spaces.
References
Subiman Kundu, Manisha Aggarwa, “Metric Spaces and Related Analysis”, World Scientific, 2024 DOI: https://doi.org/10.1142/13486
G. F. Simmons, “Introduction to Topology and Modern Analysis”, McGraw-Hill, New York, 1963.
N. L. Carothers, “Real Analysis”, Cambridge University Press, 2000. DOI: https://doi.org/10.1017/CBO9780511814228
Haim Brezis, “Functional Analysis, Sobolev Spaces and Partial Differential Equations”, Springer, 2011. DOI: https://doi.org/10.1007/978-0-387-70914-7
J. Tinsley Oden, Leszek Demkowicz, “Applied Functional Analysis”, CRC Press, 2010.
William E. Schiesser, “The Numerical Method of Lines: Integration of Partial Differential Equations”, Academic Press (Elsevier), 1991.
K. Lange and R. Carson, “EM Reconstruction Algorithms for Emission and Transmission Tomography”, Journal of Computer Assisted Tomography, Volume 8, Issue 2, Pages 306–316, 1984.
Prabha Kundur, “Power System Stability and Control”, McGraw-Hill Education, 1994.
D. Blackwell, “Discounted dynamic programming”, Annals of Mathematical Statis- tics, 36(1), 226–235, 1965. DOI: https://doi.org/10.1214/aoms/1177700285
K. Kuratowski, Sur les espaces complets, Fund. Math., 15, pp. 301–309 (1930). DOI: https://doi.org/10.4064/fm-15-1-301-309
J. A. Souza and R. W. M. Alves, Cantor–Kuratowski theorem in admissible spaces, Topology Appl., 252, pp. 158–168 (2019). DOI: https://doi.org/10.1016/j.topol.2018.11.017
Z. D. Mitrovic and I. D. Arandjelovic, Existence of generalised best approximations, Nonlinear Convex Anal., 15, pp. 787–792 (2014).
Z. D. Mitrovic and I. D. Arandjelovic, Generalized scalar equilibrium problem with applications to best and coupled best approximations, J. Fixed Point Theory Appl., 19, pp. 1613–1624 (2017). DOI: https://doi.org/10.1007/s11784-016-0396-7
C. Horvath, Measure of non-compactness and multivalued mappings in complete metric topological vector spaces, J. Math. Anal. Appl., 108, 403–408 (1985). DOI: https://doi.org/10.1016/0022-247X(85)90033-2
