Common fixed points versus invariant approximation in nonconvex sets.

Nashine, Hemant Kumar; Khan, Mohammad Saeed

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$C_{q}$ -commuting maps and invariant approximations.

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Common fixed point and invariant approximation results in certain metrizable topological vector spaces.

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Best approximation and fixed points in strong $M$ -starshaped metric spaces.

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Best approximation for nonconvex set in $q$ -normed space

Hemant Kumar Nashine (2006)

Archivum Mathematicum

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Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of $q$ -normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som (Mukherjee, R. N., Som, T., A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16(3) (1985), 243–244.) and Jungck and Sessa (Jungck, G., Sessa, S., Fixed point theorems...