The fixed point property for weakly admissible compact convex sets: searching for a solution to Schauder's conjecture

Fixed points for convex continuous mappings in topological vector spaces

“…See Klee [14], Zima [29], Rzepecki [24], Hadzic [8], [9], Idzik [11], Nguyen [16], [17], Nguyen and Le [18]. However, this problem still remains unsolved.…”

Fixed Point Theorems for Upper Semicontinuous Set-valued Mappings in p-Vector Spaces

“…Finally, we like to mention that by comparing with topological degree approach or related other methods used or developed by Askoura et al [3], Cauty [9]- [10], Nhu [31] and others, the arguments used in this section actually provides an accessible way for the study of nonlinear analysis for p-convex vector spaces (0 < p ≤ 1). The results…”

“…Cauty [9], Cauty [10], Dobrowolski [13], Li [28], Nhu [31], Okon [32], Park [35], Reich [37], Smart [42], Xiao and Lu [46], Xiao and Zhu [47], Yuan [50] under the framework of compact single-valued or upper semicontinuous set-valued mappings.…”

“…Ben-El-Mechaiekh and Saidi [7], Browder [8], Cellina [11], Chang [12], Ennassik et al [15], Fan [16]- [17], Górniewicz [19], Guo et al [20], Granas and Dugundji [21], Li [28], Liu [29], Nhu [31], Park [34]- [35], Reich [37], Smart [42],…”

Fixed Point Theorems for Upper Semicontinuous Set-valued Mappings in p-Vector Spaces

“…Ben-El-Mechaiekh and Saidi [7], Browder [8], Cellina [11], Chang [12], Ennassik et al [16], Fan [17]- [18], Górniewicz [20], Granas and Dugundji [22], Guo et al [21], Nhu [31], Park [33], Reich [35], Smart [40], Tychonoff [41], Weber [42]- [43], Xiao and Lu [44], Xiao and Zhu [45], Xu [46], Yuan [47]- [50] and many other scholars, and also see the comprehensive references and related discussion under the general framework of topological vector space, or p-vector spaces for non-self set-valued mappings (0 < p ≤ 1).…”