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: Weakly contractive multivalued maps and wdistances on complete quasi-metric spaces | Marín et al. Fixed Point Theory and Applications 2011 2011 2 http content 2011 1 2 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Weakly contractive multivalued maps and w-distances on complete quasi-metric spaces Josefa Marin Salvador Romaguera and Pedro Tirado Correspondence sromague@mat. Instituto Universitario de Matemática Pura y Aplicada Universidad Politécnica de Valencia Camino de Vera s n 46022 Valencia Spain Abstract We obtain versions of the Boyd and Wong fixed point theorem and of the Matkowski fixed point theorem for multivalued maps and w-distances on complete quasi-metric spaces. Our results generalize in several directions some well-known fixed point theorems. Keywords Fixed point multivalued map w-distance quasi-metric space Introduction and preliminaries Throughout this article the letters N and C l will denote the set of positive integer numbers and the set of non-negative integer numbers respectively. Following the terminology of 1 by a T0 quasi-pseudo-metric on a set X we mean a function d X X X 0 such that for all x y z e X i d x y d y x 0 o x y ii d x z d x y d y z . A T0 quasi-pseudo-metric d on X that satisfies the stronger condition i d x y 0 o x y is called a quasi-metric on X. Our basic references for quasi-metric spaces and related structures are 2 and 3 . We remark that in the last years several authors used the term quasi-metric to refer to a T0 quasi-pseudo-metric and the term T1 quasi-metric to refer to a quasimetric in the above sense. It is also interesting to recall see for instance 3 that T0 quasi-pseudo-metric spaces play a crucial role in some fields of theoretical computer science asymmetric functional analysis and approximation theory. Hereafter we shall simply write T0 qpm instead of T0 quasi-pseudo-metric if no confusion arises. A T0 qpm space is a pair X d such that X is a set and d is a T0 qpm on X. If d is a quasi-metric on X the pair X d is
