A Unique Common Fixed Point Theorem for a Metric Space with the Property (E.A)

K. Prudhvi^1,

¹Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, Telangana State, India

Cite this paper:
K. Prudhvi. A Unique Common Fixed Point Theorem for a Metric Space with the Property (E.A). American Journal of Applied Mathematics and Statistics. 2023; 11(1):11-12. doi: 10.12691/ajams-11-1-2

Abstract

In this paper, we prove a unique common fixed point theorem for metric space with (E.A) property. Our result is a generalization and improvement of some recent results existing in the literature [1].

Keywords:
fixed point common fixed point property (E. A) weakly compatible mappings

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References:

[1]	M. Amari and D. El. Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Appl., vol. 270, pp. 181-188, 2002.
[2]	S. Banach, Surlesoperations dans les ensembles abstraitsetleurs application auxequationsintegrales, Fund. Math. 3 (1922), 133-181 (in French).
[3]	Al-Thagafi and Shahzad, Generalized I – non expansive self maps and invariant approximations, Acta Mathematics Sinnica, vol. 24, pp. 867-876, 2008.
[4]	G. Junck, Compatible mappings and common fixed points, Int. J. Math. & Math .Sci., vol.9, pp. 771-779, 1986.
[5]	G. Junck and B. E. Rhoads, Fixed point theorems for occasionally weakly compatible mappings, Fixed point theory, vol.7, pp. 286-296, 2006.
[6]	Özen Özer, Saleh Omran, On the generalized C*-valued metric spaces related with Banach fixed point theory, International Journal of Advanced and Applied Sciences, 4(2), (2017), 35-37).
[7]	K. Prudhvi, A Unique Fixed Point Theorem on a Generalized d-Cyclic Contraction mapping in d-Metric Spaces, American Journal of Applied Mathematics and Statistics, Vol.6., No.3, (2018), 107-108.
[8]	K. Prudhvi, A common fixed point result in ordered complete cone metric spaces, American Journal of Applied Mathematics and Statistics, Vol.4, No.2 (2016), 43-45.
[9]	R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., vol. 60, pp. 251-258, 1968.
[10]	G. Junck and B. E. Rhoads, Fixed point theorems for occasionally weakly compatible mappings, Erratum Fixed point theory, vol. 977, pp.383-384, 2008.
[11]	G. Junck, Commuting mappings and fixed points, Amer. Math. Monthly, vol. 73, pp. 261-263.