AN INTRODUCTION TO 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:

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.

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Published

2021-10-15

Issue

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

Section

Articles

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