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Based on this concept, a new class of functions, named as semilocal <jats:italic>E<\/jats:italic>\u2010preinvex functions, which is a generalization of semi\u2010<jats:italic>E<\/jats:italic>\u2010preinvex functions and semilocal <jats:italic>E<\/jats:italic>\u2010convex functions, is introduced. Simultaneously, some of its basic properties are discussed. 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