A note on tvs-cone metric fixed point theory

Abstract

In this paper, the concept of set-valued contraction of Nadler type in the setting of tvs-cone spaces was introduced and a fixed point theorem in the setting of tvs-cone spaces with respect to a solid cone was proved. Obtained results extend and generalize the main results of [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific Journal of Mathematics 30 (1969) 475-488] and [D. Wardowski, On set-valued contractions of Nadler type in cone metric spaces, Applied Mathematics Letters 24 (2011) 275-278]. Two examples are given to illustrate the usability of the results. © 2011 Elsevier Ltd.