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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 931656, 17 pages
Research Article

On Upper and Lower 𝛽 ( 𝜇 𝑋 , 𝜇 𝑌 ) -Continuous Multifunctions

Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand

Received 9 May 2012; Accepted 24 June 2012

Academic Editor: B. N. Mandal

Copyright © 2012 Chawalit Boonpok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new class of multifunctions, called upper (lower) 𝛽 ( 𝜇 𝑋 , 𝜇 𝑌 ) -continuous multifunctions, has been defined and studied. Some characterizations and several properties concerning upper (lower) 𝛽 ( 𝜇 𝑋 , 𝜇 𝑌 ) -continuous multifunctions are obtained. The relationships between upper (lower) 𝛽 ( 𝜇 𝑋 , 𝜇 𝑌 ) -continuous multifunctions and some known concepts are also discussed.