Bozkurt, HacerYılmaz, Yılmaz2021-04-202021-04-202018Bozkurt, H., Yılmaz, Y. (2018). Some new properties of inner product quasilinear spaces. 3rd. International Congress on Mathematic, Engineering and Natural Sciences, 21-22 April 2018, Mardin.978-605-9885-73-7https://docs.wixstatic.com/ugd/614b1f_556323e6228440bc8c4f075a34bf7a4f.pdfhttps://hdl.handle.net/20.500.12402/2941The theory of quasilinear analysis is one of the fundamental theories in nonlinear analysis which has various applications such as integral and differential equations, approximation theory and bifurcation theory. Aseev generalized the concept of linear spaces, using the partial order relation hence they have defined the quasilinear spaces. He also described the convergence of sequences and norm in quasilinear space. Further, he introduced the concept of Ω-space which is only meaningful in normed quasilinear spaces. In the present presentation, we introduce over symmetric set on a inner product quasilinear spaces. We establish some new results related to this new concept. Further, we obtain new conclusions for orthogonal and orthonormal subspaces of inner product quasilinear spaces. These results generalize recent well known results in the linear inner product spaces. Also, some examples have been given which provide an important contribution to understand the structure of inner product quasilinear spaces.eninfo:eu-repo/semantics/closedAccessQuasilinear SpaceInner Product Quasilinear SpaceHilbert Quasilinear SpaceOrthogonalityOrthonormalityConference Object