Journal of Linear and Topological Algebra Vol. 09, No. 03, 2020, 201- 211 On weakly e ∗ -open and weakly e ∗ -closed functions M. ¨ Ozko¸ c a,* , S. Erdem b a Mu˘ gla Sıtkı Ko¸cman University, Faculty of Science, Department of Mathematics, 48000, Mente¸ se-Mu˘ gla, Turkey. b Mu˘ gla Sıtkı Ko¸cman University, Graduate School of Natural and Applied Sciences, Mathematics, 48000, Mente¸ se-Mu˘ gla, Turkey. Received 12 February 2020; Revised 12 September 2020; Accepted 17 September 2020. Communicated by Ghasem Soleimani Rad Abstract. The aim of this paper is to introduce and study two new classes of functions called weakly e * -open functions and weakly e * -closed functions via the concept of e * -open set defined by Ekici [9]. The notions of weakly e * -open and weakly e * -closed functions are weaker than the notions of weakly β-open and weakly β-closed functions defined by Caldas and Navalagi [6], respectively. Moreover, we investigate not only some of their fundamental properties, but also their relationships with other types of existing topological functions. c ⃝ 2020 IAUCTB. All rights reserved. Keywords: e * -open set, e * -open function, weakly e * -open function, weakly e * -closed function, contra e * -closed. 2010 AMS Subject Classification: 54C08, 54C10, 54C05. 1. Introduction and preliminaries The notions of open functions and closed functions are important objects of topology. Recently, many researchers have been introduced and studied weak and strong forms of these concepts such as α-open functions [16], almost open functions [21], semiopen func- tions [5], preclosed functions [12], β -open and β -closed functions [1], weakly open func- tions [19], weakly closed functions [20], preopen functions [14], weakly eR-open functions [18]. After then, the concepts of weakly β -open and weakly β -closed functions which are * Corresponding author. E-mail address: murad.ozkoc@mu.edu.tr, murad.ozkoc@gmail.com (M. ¨ Ozko¸c); seraperdem@posta.mu.edu.tr, ser- aperdem123@gmail.com (S. Erdem). Print ISSN: 2252-0201 c ⃝ 2020 IAUCTB. All rights reserved. Online ISSN: 2345-5934 http://jlta.iauctb.ac.ir