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Best approximation and fixed points for rational-type contraction mappings

Chandok Sumit

Journal of Applied Analysis

2019

Vol. 25, nr 2

205--209

In this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski-Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.

Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation

Chandok S., Narang T.D.

Journal of Applied Analysis

2012

Vol. 18, nr 1

33-46

We prove some new results on the existence of common fixed points for nonexpansive and asymptotically nonexpansive mappings in the framework of convex metric spaces. We also obtain some results on common fixed points from the set of best and best simultaneous approximations as applications. The proved results generalize and extend some of the known results in the literature.

On convex hulls of star sets

Herburt I.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 4

433-440

We prove that the operation conv of taking a convex hull is continuous but is not Lipschitz continuous with respect to the radial metric for the class of star sets at 0 with 0 in interiors.