Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 6 (2011), 107 -- 116


Bessem Samet and Calogero Vetro

Abstract. Recently, Azam, Arshad and Beg [4] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result.

2010 Mathematics Subject Classification: 54H25; 47H10; 34B15.
Keywords: Fixed point; C-chainable cone rectangular metric space; Uniformly locally contractive mappings.

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B. Samet
Ecole Supérieure des Sciences et Techniques de Tunis, Département de Mathématiques
5, Avenue Taha Hussein-Tunis,
B.P.:56, Bab Menara-1008, Tunisie.

C. Vetro
Dipartimento di Matematica e Informatica, Università degli Studi di Palermo
Via Archirafi 34,
90123 Palermo, Italy.