Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Q-Functions on Quasimetric Spaces and Fixed Points for Multivalued Maps | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 603861 10 pages doi 2011 603861 Research Article Q-Functions on Quasimetric Spaces and Fixed Points for Multivalued Maps J. Marin S. Romaguera and P. Tirado Instituto Universitario de Matemdtica Pura y Aplicada Universidad Politecnica de Valencia Camino de Vera s n 46022 Valencia Spain Correspondence should be addressed to S. Romaguera sromague@ Received 14 December 2010 Revised 26 January 2011 Accepted 31 January 2011 Academic Editor Qamrul Hasan Ansari Copyright 2011 J. Marin et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We discuss several properties of Q-functions in the sense of Al-Homidan et al. In particular we prove that the partial metric induced by any T0 weighted quasipseudometric space is a Q-function and show that both the Sorgenfrey line and the Kofner plane provide significant examples of quasimetric spaces for which the associated supremum metric is a Q-function. In this context we also obtain some fixed point results for multivalued maps by using Bianchini-Grandolfi gauge functions. 1. Introduction and Preliminaries Kada et al. introduced in 1 the concept of -distance on a metric space and extended the Caristi-Kirk fixed point theorem 2 the Ekeland variation principle 3 and the nonconvex minimization theorem 4 for -distances. Recently Al-Homidan et al. introduced in 5 the notion of Q-function on a quasimetric space and then successfully obtained a Caristi-Kirk-type fixed point theorem a Takahashi minimization theorem an equilibrium version of Ekeland-type variational principle and a version of Nadler s fixed point theorem for a Q-function on a complete quasimetric space generalizing in this way among others the main results of 1 because every -distance is in fact a .
