en نتایجی روی فضاهای نرمدار مخروطی تخصصي Special پژوهشي Research paper <p>In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we introduce the notion of algebraically cone metric and we will show that every algebraically cone metric space has a topology.</p> Cone bounded, Equivalent cone norms, Algebraically cone metric. 71 80 http://ijmsi.ir/browse.php?a_code=A-10-380-1&slc_lang=en&sid=1 Assadollah Niknam 10031947532846002281 10031947532846002281 No professor Saeedeh Shamsi Gamchi 10031947532846002282 10031947532846002282 Yes Ph.D student Mohammad Janfada 10031947532846002283 10031947532846002283 No associate professor