TY - JOUR

T1 - Normed ordered and E-metric spaces

AU - Al-Rawashdeh, Ahmed

AU - Shatanawi, Wasfi

AU - Khandaqji, Muna

PY - 2012

Y1 - 2012

N2 - In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space E, and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of , and we discuss their extension to E. We introduce the notion of E -metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of convergence and Cauchy theory. In particular, we get a fixed point theorem of a contractive mapping in E -metric spaces. Finally, by extending the notion of a contractive sequence in a real-valued metric space, we show that in E -metric spaces, a contractive sequence is Cauchy.

AB - In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space E, and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of , and we discuss their extension to E. We introduce the notion of E -metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of convergence and Cauchy theory. In particular, we get a fixed point theorem of a contractive mapping in E -metric spaces. Finally, by extending the notion of a contractive sequence in a real-valued metric space, we show that in E -metric spaces, a contractive sequence is Cauchy.

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U2 - 10.1155/2012/272137

DO - 10.1155/2012/272137

M3 - Article

AN - SCOPUS:84862288423

VL - 2012

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 272137

ER -