Coupled fixed point results under tvs-cone metric and w-cone-distance

Abstract

In this paper, we first give an easy positive answer to a questionconcerning quasicontractions under w-cone-distance, posed in therecent paper [Lj. Ciric, H. Lakzian, V. Rakov cevic, Fixed point theorems for w-cone distance contraction mappings intvs-cone metric spaces, Fixed Point Theory Appl. 2012:3 (2012), doi:10.1186/1687-1812-2012-3]. Then, we prove some coupled and b-coupled fixed point results in tvs-cone metric spaces, which improve several known corresponding results. Finally, we derive several (common) coupled fixed point results under $w$-cone distance in tvs-cone metric spaces, thus also improving some known theorems. Examples are given to show the usage of these results, and that our improvements are proper.