AN INTRODUCTION TO $\mathfrak{U}$-METRIC SPACE AND NON-LINEAR CONTRACTION WITH APPLICATION TO THE STABILITY OF FIXED POINT EQUATION

Authors

  • K. Roy Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India Author
  • M. Saha Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India Author
  • D. Dey Sudpur High School(H.S), Purba Bardhaman-713150, West Bengal, India Author

Keywords:

$\mathfrak{U}$-metric space, Cantor's intersection like theorem, fixed point, stability of fixed point equation

Subjects:

47H10, 54H25

Abstract

In this paper, we introduce the notion of $U$-metric space of $n$-tuples which generalizes several known metric-type spaces.We study topological properties of such newly constructed spaces and prove Cantor's intersection-like theorem.Banach contraction principle theorem is proved in this space and we apply the theorem to obtain the stability of a fixed point equation.

Downloads

Published

2021-10-15

Issue

Vol. 73 No. 4 (2021): Vol. 73, Issue 4

Section

Articles

License

Copyright (c) 2021 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.