University of MaraghehSahand Communications in Mathematical Analysis2322-580720120230101Pseudosymmetric Spaces as Generalization of Symmetric spaces617969706710.22130/scma.2022.551403.1090ENBilal BilalovDepartment of Non-harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.0000-0003-0750-9339Yusuf ZerenDepartment of Mathematics, Yildiz Technical University, Istanbul, Turkey.0000-0001-8346-2208Betule AlizadeDepartment of Non-harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.Feyza Elif DalDepartment of Mathematics, Yildiz Technical University, Istanbul, Turkey.Journal Article20220405In this paper, the concept of a pseudosymmetric space which is a natural generalization of the concept of a symmetric space is defined. All basic concepts such as the Luxemburg representation theorem, the Boyd indices, the fundamental function and its properties, Calderon's theorem, etc., is transferred over the pseudosymmetric case. Examples are given for pseudosymmetric spaces. The quasi-symmetric spaces expand the scope of the application of symmetric space results.https://scma.maragheh.ac.ir/article_697067_b31352720c729361372e367750858f7f.pdf