In this paper, we introduce and study upper and lower slightly beta-continuous multifunctions as a generalization of upper (lower) semicontinuous, upper (lower) alfa-continuous, upper (lower) precontinuous, upper (lower) quasi-continuous, upper (lower) gamma-continuous, upper (lower) beta-continuous multifunctions and slightly beta-continuous functions. Some characterizations and several properties concerning upper (lower) slightly beta-continuous multifunctions are obtained. Furthermore, the relationships between upper (lower) slightly beta-continuous multifunctions and other related multifunctions are also discussed.
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