This paper aims at proving the Banach's contraction theorem in a 2-metric space by repeated use of the symmetry and the tetrahedron inequality of the 2-metric, based on only an elementary greatest lower bound property instead of usual iteration procedure.

Phaneendra T

Department of Mathematics

School of Advanced Sciences

Vellore Campus

K. Kumara Swamy

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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Journal	Proceedings of the Jangjeon Mathematical Society
Publisher	Jangjeon Research Institute for Mathematical Sciences and Physics
ISSN	15987264