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Fixed points and best approximation in Menger convex metric spaces

Ismat Beg, Mujahid Abbas (2005)

Archivum Mathematicum

We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and quasi nonexpansive maps defined on a compact convex subset of a uniformly convex complete metric space. We obtain results on best approximation as a fixed point in a strictly convex metric space.

Fixed points for cyclic orbital generalized contractions on complete metric spaces

Erdal Karapınar, Salvador Romaguera, Kenan Taş (2013)

Open Mathematics

We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some...

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