On the ray-walker extension of the Caristi-Kirk fixed point theorem

Function variational principles and coercivity

“…Since the opposite implication is also true, it will follow that these (relative type) statements are logically equivalent. The specific tools of our developments are the concept of normal function and a construction emerging from the fixed point one in Park and Bae [19] (cf. Section 3).…”

Some Results Related to Caristi's Fixed Point Theorem and Ekeland's Variational Principle

“…• (ii) Since the usual metric space is a special case of a fuzzy metric space (see [13]), therefore when X is a complete metric space, the corresponding results of [3 -5] and [16,17] may be recovered as a special cases of our results.…”

“…Caristi's fixed point theorem [3, Theorem (2.1)'] and its equivalent Ekeland's vaxiational principle [6, Theorem 1.1], which was not basically formulated as a fixed point theorem, and is an abstraction of a lemma of Bishop and Phelps [1] (see also [2]), have been of continuing interest in fixed point theory because of their numerous applications (see [4], [5], [8]- [10], [14]- [17]). Recently Jung et.…”

Function Variational Principles and Normed Minimizers

“…Summing up, (ZVP) includes (EVP); but the provided argument is rather involved. A simplification of the proposed reasoning was given in Turinici [26], by a technique developed in Park and Bae [20]; note that, as a consequence of this, (ZVP) is nothing but a logical equivalent of (EVP).…”