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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.

Approximation of functions and their conjugates in Lp and uniform metric by Euler means

Volosivets S. S., Tyuleneva A. A.

Demonstratio Mathematica

2018

Vol. 51, nr 1

141--150

For 2π-periodic functions from Lp (where 1 < p < ∞) we prove an estimate of approximation by Euler means in Lp metric generalizing a result of L. Rempuska and K. Tomczak. Furthermore, we show that this estimate is sharp in a certain sense. We study the uniform approximation of functions by Euler means in terms of their best approximations in p-variational metric and also prove the sharpness of this estimate under some conditions. Similar problems are treated for conjugate functions.

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.