Bilal Bilalov - Department of Non-harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
Yusuf Zeren - Department of Mathematics, Yildiz Technical University, Istanbul, Turkey.
Betule Alizade - Department of Non-harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
Feyza Elif Dal - Department of Mathematics, Yildiz Technical University, Istanbul, Turkey.

In 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.

Symmetric spaces, Calderon theorem, Boyd indices, fundamental function