COMMON FIXED POINT THEOREMS FOR FOUR SELFMAPS OF A COMPLETE D*- METRIC SPACE
Upender S
Vol. 3, Issue 1, Jan-Dec 2017
Page Number: 136 - 149
Abstract:
Suppose (X, D*) is a D*- metric space and S, T, I and J are selfmaps of X. If these four maps and the space X satisfy certain conditions, we shall prove that they have a unique common fixed point in this paper. As a consequence we deduce a common fixed point theorem for four selfmaps of a complete D*- metric space. Further, we show that a common fixed point theorem for four selfmaps of a metric space proved by Brain Fisher ([5]) follows as a particular case of the theorem.
References
- Ahmad, B., Ashraf, M., & Rhoades, B. E. (2001). Fixed point theorems for expansive mappings in D-metric spaces. Indian Journal of Pure and Applied Mathematics, 32(10), 1513–1518.
- Dhage, B. C. (1992). Generalised metric spaces and mappings with fixed point. Bulletin of the Calcutta Mathematical Society, 84(4), 329–336.
- Dhage, B. C. (1999). A common fixed point principle in D-metric spaces. Bulletin of the Calcutta Mathematical Society, 91(6), 475–480.
- 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/S0161171200001587
- Fisher, B. (1983). Common fixed points of four mappings. Bulletin of the Institute of Mathematics, Academia Sinica, 11, 103–113.
- Naidu, S. V. R., Rao, K. P. R., & Srinivasa Rao, N. (2004). On the topology of D-metric spaces and generation of D-metric spaces from metric spaces. International Journal of Mathematics and Mathematical Sciences, 2004(51), 2719– 2740. https://doi.org/10.1155/S0161171204311257
- Naidu, S. V. R., Rao, K. P. R., & Srinivasa Rao, N. (2005). On the concepts of balls in a Dmetric space. International Journal of Mathematics and Mathematical Sciences, 2005(1), 133–141. https://doi.org/10.1155/IJMMS.2005.133
- 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
- Sedghi, S., Shobe, N., & Zhou, H. (2007). A common fixed point theorem in D*-metric spaces. Fixed Point Theory and Applications, 2007, Article ID 027906. https://doi.org/10.1155/2007/27906
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