Fixed Point Theory and Best Approximation: The KKM-map Principle

Abstract

To our parents and especially to Shri Mahadeo Singh on the occasion of his 95th birthday.

Fixed point for completely norm space and map Tɑ

“…Park [14] and Zeqing Liu, Li Wang, Shin Min Kang, and Yong Soo Kim [11]. Also, we obtain some result on its.…”

Best proximity problems for Ćirić type multivalued operators satisfying a cyclic condition

“…For details concerning the above notions see [7], [9] and [11]. Several types of comparison functions have been considered in literature.…”

Some general principles in tropical convexities

“…Most of these results can be extended to topological convex spaces whose polytopes are homothopically trivial. One of these results is as easily stated as it is fundamental, in its classical version it can be seen as an avatar of Brouwer's fixed point theorem: it is the Knaster-Kuratowski-Mazurkiewicz theorem, also known as the KKM Lemma, whose standard form can be found in [15], [1], [2], [7] or [28] along with its various forms and applications. The classical "KKM Lemma" reads as follows:…”