An application of a fixed-point theorem to approximation theory

An extension of a theorem of Sahab, Khan, and Sessa

“…An application of new result is presented to best approximation theory; our work extends earlier results of Brosowski [3], Sahab et al [12], Singh [14] and many others.…”

“…(ii) Commuting maps satisfy (2.6) so Theorem 2.3(i) is a proper generalization of the main results of Sahab et al [12] and Singh [14].…”

Common Fixed Point and Invariant Approximation in Menger Convex Metric Spaces

“…Subsequently, several interesting and valuable results appeared in the literature of approximation theory ( [1], [21] and [22]). In this section, we obtain results on best approximation as a fixed point of C q -commuting and uniformly C q -commuting mappings in the setting of a Menger convex metric space.…”

Invariant Random Approximation in Nonconvex Domain

“…To achieve the goal, the contractive jointly continuous family property given by Dotson [6] has been used. By doing so, random version results of certain invariant approximation theorems obtained by Mukherjee and Som [13] and Singh [17] have been obtained.…”

“…Later on, a number of results were developed along this direction under different conditions (see, e.g. [9,12,17]). …”