DOI: 10.24193/fpt-ro.2024.1.20

Authors: V. Sankar Raj and S. Gomathi

Abstract: The well-known Kirk [8] fixed point theorem for nonexpansive mapping relies on the geometric notion called normal structure property. Göhde [5] provided sufficient conditions for the existence of a fixed point of a nonexpansive mapping without using normal structure property. In [4], Kirk et.al. introduced a notion called relatively nonexpansive mapping and provided sufficient conditions for the existence of best proximity points for such mappings using the proximal normal structure property. The main result of this manuscript provides the existence of best proximity points of a relatively nonexpansive mapping without using the proximal normal structure property. Also, our main result extends Göhde's fixed point theorem in best proximity point setting. An example is given to illustrate our main result.

Key Words and Phrases: Göhde's fixed point theorem, cyclic contraction, relatively nonexpansive mappings, fixed points, best proximity points.

2010 Mathematics Subject Classification: 47H09, 47H10.

Published on-line: February 1st, 2024.

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