GIJASH

Galore International Journal of Applied Sciences and Humanities

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Research Paper

Year: 2017 | Month: April-June | Volume: 1 | Issue: 2 | Pages: 25-32

Characterizations of Rotundities of Normed Spaces by Means of Their d - Properties

Gaj Ram Damai1, Dr. Prakash Muni Bajracharya2

1Sidhhnath Science Campus, Mahendranagar, Tribhuvan University, Nepal.
2Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu, Nepal

Corresponding Author: Gaj Ram Damai

ABSTRACT

The notion of d-property has been defined by the authors Sankar Raj V. and Eldred A. A. Inspired by it, we define three other new notions called; LUR d-property, UR d- property, and URED d-property. We use these notions in the characterizations of rotund spaces, locally uniformly rotund spaces, uniformly rotund spaces, and normed spaces that are uniformly rotund in every direction respectively. We use the characterizations of these rotundities to prove the best proximity point theorems of various contraction mappings.

Key words: d- properties, R norm, LUR norm, UR norm, URED norm

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