On S-KKM Property and-Related Topics

Abstract

Ž. We introduce the class S-KKM X, Y, Z consisting of all multifunctions T : Y ª 2 Z that have the S-KKM property and establish a fixed-point theorem for Ž . compact and closed T in S-KKM X, Y, Z that generalizes a large number of classical fixed-point theorems. We also deduce some KKM-type theorems with application to the generalizations of the Ky Fan matching theorem and the Fan᎐Browder fixed-point theorem. ᮊ 1999 Academic Press

Fixed point theorems for better admissible multimaps on abstract convex spaces

“…(1) The concept of the better admissible class B + unifies and extends the B(X, Y ) for a G-convex space defined in Park [15], the admissible class A K C (X, Y ) defined in Park [3] and the S-KKM class in Chang et al [2].…”

Coincidence theorems and minimax inequalities in abstract convex spaces

“…More details can be found in [13,15,[21][22][23][24] and [22] and references therein. Definition 2.5 [14].…”

“…Motivated by the results of Chang et al [23], we introduce a new definition about the family of multimaps with the ms-KKMC (ms-KKMO) property in minimal abstract convex space as follows.…”

Coincidence and fixed point theorems for functions in S-KKM class on generalized convex spaces

“…On the other hand, Huang together with Chang et al [3] introduced the S-KKM class which is much larger than the class U k c . A lot of interesting and generalized results about fixed point theory on locally convex topological vector spaces have been studied in the setting of S-KKM class in [3]. In this paper, we will at first construct a coincidence theorem in S-KKM class on generalized convex spaces by means of the basic defining property for multimaps in S-KKM class.…”