Some Results on Multivalued Mappings and Inequalities Without Convexity
Charles D. Horvath · 2023
INTRODUCTION . The classical KKM theorem can be stated thus: Theorem A: Let R 0 ,…,R A be eloaed awbaeto of the standard n dineneionat simpiex and let {e 0 , e n } be the set of its vertices. If the convex hull of any subset {e https://www.w3.org/1998/Math/MathML" display="inline"> 1 1 , … + F k } https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003420040/c1be22b7-0baa-4fe4-8019-4a9594858694/content/ieq0491.tif "/> is contained in https://www.w3.org/1998/Math/MathML" display="inline"> ∪ j = 0 k R i j https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003420040/c1be22b7-0baa-4fe4-8019-4a9594858694/content/ieq0492.tif "/> then https://www.w3.org/1998/Math/MathML" display="inline"> ∪ i = 0 n R i ≠ ∅ . https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003420040/c1be22b7-0baa-4fe4-8019-4a9594858694/content/ieq0493.tif "/> This result was first extended to infinite dimensional vector sęaces by Ky Fan [ 4 ] and then by Dugundji-Granas [ 3 ].