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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: Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications | Doric and Lazovic Fixed Point Theory and Applications 2011 2011 40 http www.fixedpointtheoryandapplications.eom content 2011 1 40 RESEARCH Fixed Point Theory and Applications a SpringerOpen Journal Open Access Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications Dragan Doric and Rade Lazovic Correspondence djoricd@fon.bg. ac.rs Department of Mathematics Faculty of Organizational Sciences University of Belgrade 11000 Beograd Jove Ilica 154 Serbia Abstract In this article we obtain a Suzuki-type generalization of a fixed point theorem for generalized multivalued mappings of Ciric Matematicki Vesnik 9 24 265-272 1972 . The obtained results extend furthermore the recently developed Kikkawa-Suzuki-type contractions. Applications to certain functional equations arising in dynamic programming are also considered. Keywords Complete metric space fixed point multivalued mapping functional equation 1 Introduction and preliminaries In 2008 Suzuki 1 introduced a new type of mappings which generalize the well-known Banach contraction principle 2 . Some others 3 generalized Kannan mappings 4 . Theorem 1.1. Kikkawa and Suzuki 3 Let T be a mapping on complete metric space X d and let Ộ be a non-increasing function from 0 1 into 1 2 1 defined by p r 1 1 1 if 0 r 42 1 if r 1. 72 Let a e 0 1 2 and r a 1 - a e 0 1 . Suppose that p r d x Tx d x y implies d Tx Ty ad x Tx ad y Ty 1 for all x y e X. Then T has a unique fixed point z and limn Tnx z holds for every x e X. Theorem 1.2. Kikkawa and Suzuki 3 Let T be a mapping on complete metric space X d and 0 be a nonincreasing function from 0 1 onto 1 2 1 defined by 0 r 1 1 - r 12 1 1 r if 0 r 2 5 - 1 if V5 - 1 r -V 1 if - r 1. 42 Springer 2011 Doricc and Lazovicc licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium .
