Open Access Research

On set-valued contractions of Nadler type in tυs-G-cone metric spaces

Chi-Ming Chen

Author Affiliations

Department of Applied Mathematics, National Hsinchu University of Education, No. 521 Nanda Rd., Hsinchu City 300, Taiwan

Fixed Point Theory and Applications 2012, 2012:52 doi:10.1186/1687-1812-2012-52

Published: 26 March 2012

Abstract

In this article, for a tυs-G-cone metric space (X, G) and for the family of subsets of X, we introduce a new notion of the <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2012/1/52/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2012/1/52/mathml/M2">View MathML</a> metric with respect to G, and we get a fixed result for the stronger Meir-Keeler-G-cone-type function in a complete tυs-G-cone metric space <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2012/1/52/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2012/1/52/mathml/M4">View MathML</a> Our result generalizes some recent results due to Dariusz Wardowski and Radonevic' et al.

MSC: 47H10; 54C60; 54H25; 55M20.

Keywords:
fixed point theorem; stronger Meir-Keeler-G-cone-type function; tυs-G-cone metric space