Details

Common Fixed Point Theorems for Four Selfmaps of a Compact S−Metric Space

Upender S

Associate Professor of Mathematics, Tara Government College (Autonomous), Sangareddy - 502001, India

73-82

Vol: 11, Issue: 2, 2021

Receiving Date: 2021-05-19 Acceptance Date:

2021-06-19

Publication Date:

2021-06-27

Download PDF

http://doi.org/10.37648/ijrst.v11i02.007

Abstract

The purpose of this paper is to prove a common fixed point theorem for four selfmaps on a S–metric space and deduce a common fixed point theorem for four selfmaps on a compact S–metric space. Further we show that a common fixed point theorem for four selfmaps of a metric space prove by Brian Fisher ([5]) is a particular case of our theorem.

Keywords: S-metric space; Compatible; Fixed point theorem.

References

  1. Aliouche, A., Sedghi, S., & Shobe, N. (2012). A generalization of fixed point theorems in $S$- metric spaces. Matematički Vesnik, *64*(249), 258–266. http://eudml.org/doc/253803
  2. Dhage, B. C. (1992). Generalised metric spaces and mappings with fixed point. Bulletin of the Calcutta Mathematical Society, *84*(4), 329– 336.
  3. Dhage, B. C. (1999). A common fixed point principle in D- metric spaces. Bulletin of the Calcutta Mathematical Society, *91*(6), 475– 480.
  4. Dhage, B. C., Pathan, A. M., & Rhoades, B. E. (2000). A general existence principle for fixed point theorems in D- metric spaces. International Journal of Mathematics and Mathematical Sciences, *23*(7), 441– 448. https://doi.org/10.1155/S016117120000158 7
  5. Fisher, B. (1983). Common fixed points of four mappings. Bulletin of the Institute of Mathematics, Academia Sinica, *11*, 103–113.
  6. Gahler, S. (1963). 2-metrische Raume und iher topoloische Struktur. Mathematische Nachrichten, *26*, 115–148.
  7. Naidu, S. V. R., Rao, K. P. R., & Srinivasa Rao, N. (2004). On the topology of D- metric spaces and Generalization of D- metric spaces from Metric Spaces. International Journal of Mathematics and Mathematical Sciences, *2004*(51), 2719–2740. https://doi.org/10.1155/S01611712043112 572740. https://doi.org/10.1155/S01611712043112 57
  8. Naidu, S. V. R., Rao, K. P. R., & Srinivasa Rao, N. (2005). On the concepts of balls in a Dmetric spaces. International Journal of Mathematics and Mathematical Sciences, *2005*(1), 133– 141. https://doi.org/10.1155/IJMMS.2005.133
  9. Naidu, S. V. R., Rao, K. P. R., & Srinivasa Rao, N. (2005). On convergent sequences and fixed point theorems in D- metric spaces. International Journal of Mathematics and Mathematical Sciences, *2005*(12), 1969– 1988. https://doi.org/10.1155/IJMMS.2005.1969
  10. Rhoades, B. E., Ahmad, B., & Ashraf, M. (2001). Fixed point theorems for expansive mappings in D- metric spaces. Indian Journal of Pure and Applied Mathematics, *32*(10), 1513– 1518.
  11. Sedghi, S., Shobe, N., & Zhou, H. (2007). A common fixed point theorem in D*-metric spaces. Fixed Point Theory and Applications, *2007*, Article ID 27906. https://doi.org/10.1155/2007/27906
Back

Disclaimer: Indexing of published papers is subject to the evaluation and acceptance criteria of the respective indexing agencies. While we strive to maintain high academic and editorial standards, International Journal of Research in Science and Technology does not guarantee the indexing of any published paper. Acceptance and inclusion in indexing databases are determined by the quality, originality, and relevance of the paper, and are at the sole discretion of the indexing bodies.

We are one of the best in the field of watches and we take care of the needs of our customers and produce replica watches of very good quality as per their demands.