Best proximity pair and fixed point results for noncyclic mappings in convex metric spaces | Zendy

Moosa Gabeleh | Zendy; Naseer Shahzad | Zendy

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Best proximity pair and fixed point results for noncyclic mappings in convex metric spaces

Author(s) -

Moosa Gabeleh,

Naseer Shahzad

Publication year - 2016

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1612149g

Subject(s) - mathematics , pointwise , convexity , metric space , convex metric space , regular polygon , pure mathematics , metric (unit) , space (punctuation) , discrete mathematics , mathematical analysis , geometry , computer science , operations management , financial economics , economics , operating system

In this article, we formulate a best proximity pair theorem for noncyclic relatively nonexpansive mappings in convex metrc spaces by using a geometric notion of semi-normal structure. In this way, we generalize a corresponding result in [W. Takahashi, A convexity in metric space and nonexpansive mappings, KODAI MATH. SEM. REP. 22 (1970) 142-149]. We also establish a best proximity pair theorem for pointwise noncyclic contractions in the setting of convex metric spaces. Our result generalizes a result due to Sankara Raju Kosuru and Veeramani [G. Sankara Raju Kosuru and P. Veeramani, A note on existence and convergence of best proximity points for pointwise cyclic contractions, Numer. Funct. Anal. Optim., 82 (2011) 821-830].

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