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In this paper, we introduce the new notions called \breve{\mathbit{\theta}}-\mathbf{I}-locally closed sets, \breve{\mathbit{\theta}}-\mathbf{I}-locally closed sets and \breve{\mathbit{\theta}}-\mathbf{I}-closed functions and investigated their properties and also we have studied their relations to the other types of locally closed sets with suitable examples. Finally we introduce the notion \breve{\mathbit{\theta}}-\mathbf{I}-submaximal spaces and also investigated the properties with examples.