Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem

Details Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem

2011-02-10

arxiv.org/abs/1102.2093v1

Mathematics

General Topology

Scientific paper

Rectangular TVS-cone metric spaces are introduced and Kannan's fixed point theorem is proved in these spaces. Two approaches are followed for the proof. At first we prove the theorem by a direct method using the structure of the space itself. Secondly, we use the nonlinear scalarization used recently by Wei-Shih Du in [A note on cone metric fixed point theory and its equivalence, {Nonlinear Analysis},72(5),2259-2261 (2010).] to prove the equivalence of the Banach contraction principle in cone metric spaces and usual metric spaces. The proof is done without any normality assumption on the cone of the locally convex topological vector space, and hence generalizing several previously obtained results.

Affiliated with

Also associated with

No associations

Rating

Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-694347