Equivalents of Ordered Fixed Point Theorems of Kirk, Caristi, Nadler, Banach, and others

Abstract

Recently, we improved our long-standing Metatheorem in Fixed Point Theory. In this paper, as its applications, some well-known order theoretic fixed point theo- rems are equivalently formulated to existence theorems on maximal elements, com- mon fixed points, common stationary points, and others. Such theorems are the ones due to Banach, Nadler, Browder-Göhde-Kirk, Caristi-Kirk, Caristi, Brøndsted, and possibly many others.

Keywords

• fixed point theorem
• pre-order metric space
• fixed point
• stationary point
• stationary point
• maximal element

Kaynakça

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