Existence of invariant points and applications to simultaneous approximation

Abstract

For the set of e-simultaneous approximation and e-simultaneous coapproximation, we derive certain Brosowski-Meinardus type invariant point results in this paper. As a consequence, some results on e-approximation, e-coapproximation, best approximation, and best coapproximation are also deduced.

Keywords

• e-simultaneous approximately compact set
• star shaped set
• best approximation
• best simultaneous approximation
• e-simultaneous approximation