A fixed point theorem in a lattice ordered semigroup cone valued cone metric spaces

Volume 6, Issue 4, pp 285--292 http://dx.doi.org/10.22436/jnsa.006.04.06

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Authors

K. P. R. Sastry - 8-28-8/1, Tamil street, Chinna Waltair, Visakhapatnam--530 017, India. Ch. Srinivasa Rao - Department of Mathematics, Mrs. A. V. N. College, Visakhapatnam--530 001, India. A. Chandra Sekhar - Department of Mathematics, GIT, Gitam University, Visakhapatnam--530 045, India. M. Balaiah - Department of Mathematics, Srinivasa Institute of Engineering & Technology, N. H. 216, Cheyyeru, Amalapuram, East Godavari (Dist), 533 222, India.

Abstract

In this paper, we introduce the notion of a cone which is a lattice ordered semigroup (l.o.s.g. cone) in a real Banach space, obtain certain preliminary results on such cones and obtain a fixed point theorem on a cone metric space with l.o.s.g. cone which eventually extends a result of Filipovic et. al. [M. Filipović, L. Paunović, S. Radenović and M. Rajović, Math. Compu. Model. 54 (2011), 1467-1472] to cone metric spaces equipped with l.o.s.g. cone.

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Keywords

• Cone metric space
• Comparison function
• Lattice ordered semigroup
• l.o.s.g. cone
• Coincidence point
• Fixed point.

MSC

•  47H10
•  54H25

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