Abstract

The present research paper aims to establish some generalized Banach fixed point theorems on closed Hilbert spaces using the sequence of mappings and satisfying the Banach Fixed point Property. The Banach fixed point theory plays an important role in modern areas of mathematics, mathematical Science, and different branches of Science. Koparde P. V; Waghmode B. B [5]; Pandhar, M. D and Waghmode, B. B [6] have established some Banach Fixed point theorems on a sequence of mappings on a closed subset S of a Hilbert space H. After that, Veerapandi, T and Kumar, S. A. [9] have introduced some fruitful results in this line. In this research article, some generalized Banach fixed point theorems of Veerapandi, T and Kumar, S. A. [9] are stated above. The mathematician established a theory on Hilbert spaces in sequences of mappings on closed spaces.

Keywords

References

[1] Stefan Banach, “On Operations in Abstract Sets and their Application to Integral Equations,” Foundations of Mathematics, vol. 3, pp. 133-181, 1922.
[Google Scholar]
[2] V.H. Badshah, and G. Meena, “Common Fixed Point Theorems of an Infinite Sequence of Mappings,” Chh. J. Sci. Tech, vol. 2, pp. 87-90, 2005.
[Google Scholar]
[3] B. Fisher, “Common Fixed Point Mappings,” Indian Journal of Mathematics, vol. 20, no. 2, pp. 135-137, 1978.
[Google Scholar] 
[4] K. Kalyani, N. Seshagiri Rao, and K.V.L.N. Acharyulu, “A Fixed Point of Self-Mapping in Hilbert Space,” Global Journal of Pure and Applied Mathematics, vol. 10, no. 6, pp. 783-786, 2014.
[Google Scholar]
[5] D.M. Pandhare, and B.B. Waghmode, “On Sequence of Mappings in Hilbert Space,” Mathematics Education, vol. 32, pp. 61-63, 1998.
[Google Scholar]
[6] D.M. Pandhare, and B.B. Waghmode, “A Common Fixed Point Theorem in Hilbert Space,” Acta Ciencia Indica, vol. 23, no. 2, pp. 107-110, 1997.
[Google Scholar]
[7] N. Seshagiri Rao, and K. Kalyani, “Generalized Fixed Point Theorems of Pandhar and Waghmode in Hilbert Space,” Electronic Journal of Mathematical Analysis and Applications, vol. 8, no. 2, pp. 188-197, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[8] A.K. Sharma, V.H. Babshah, and V.K. Gupta, “Common Fixed Point Theorems of a Sequence of Mappings in Hilbert Spaces,” Journal of Ultra Scientist of Physical Sciences, vol. 23, no. 3A, pp. 790-794, 2012.
[Google Scholar]
[9] T. Veerapandi, and S.A. Kumar, “Common Fixed Point Theorems of a Sequence of Mappings on Hilbert Space,” Bulletin of Calcutta Mathematical Society, vol. 91, no. 4, pp. 299-308, 1999.
[Google Scholar]