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

Sastry, K. P. R.¹ ; Rao, Ch. Srinivasa² ; Sekhar, A. Chandra³ ; Balaiah, M.⁴

¹ 8-28-8/1, Tamil street, Chinna Waltair, Visakhapatnam--530 017, India
² Department of Mathematics, Mrs. A. V. N. College, Visakhapatnam--530 001, India
³ Department of Mathematics, GIT, Gitam University, Visakhapatnam--530 045, India
⁴ Department of Mathematics, Srinivasa Institute of Engineering & Technology, N. H. 216, Cheyyeru, Amalapuram, East Godavari (Dist), 533 222, India

Journal of nonlinear sciences and its applications, Tome 6 (2013) no. 4, p. 285-292.

Résumé

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.

Détail

DOI : 10.22436/jnsa.006.04.06

Classification : 47H10, 54H25
Keywords: Cone metric space, Comparison function, Lattice ordered semigroup, l.o.s.g. cone, Coincidence point, Fixed point.

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