SOME RESULTS ON TVS-CONE NORMED SPACES AND ALGEBRAIC CONE METRIC SPACES

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NIKNAM ASSADOLLAH; SHAMSI GAMCHI SAEEDEH; JANFADA MOHAMMAD

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS Year:2014 | Volume:9 | Issue:1 Page(s): 71-80

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Title

SOME RESULTS ON TVS-CONE NORMED SPACES AND ALGEBRAIC CONE METRIC SPACES

Author(s)

NIKNAM ASSADOLLAH | SHAMSI GAMCHI SAEEDEH | JANFADA MOHAMMAD | Issue Writer Certificate

Keywords

CONE BOUNDED

EQUIVALENT CONE NORMS

ALGEBRAIC CONE METRIC

Abstract

In this paper we introduce the cone bounded linear mapping and 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 TVS-cone norms are equivalent if and only if they induce equivalent topologies. In the sequel, the notion of algebraic cone metric is introduced and it is shown that every algebraic cone metric space has a topology and the Banach fixed point theorem for contraction mappings on algebraic cone metric spaces is proved.

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Cites

STRONGLY ALMOST IDEAL CONVERGENT SEQUENCES IN A LOCALLY CONVEX SPACE DEFINED BY MUSIELAK-ORLICZ FUNCTION

References

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APA: Copy

NIKNAM, ASSADOLLAH, SHAMSI GAMCHI, SAEEDEH, & JANFADA, MOHAMMAD. (2014). SOME RESULTS ON TVS-CONE NORMED SPACES AND ALGEBRAIC CONE METRIC SPACES. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 9(1), 71-80. SID. https://sid.ir/paper/310370/en

Vancouver: Copy

NIKNAM ASSADOLLAH, SHAMSI GAMCHI SAEEDEH, JANFADA MOHAMMAD. SOME RESULTS ON TVS-CONE NORMED SPACES AND ALGEBRAIC CONE METRIC SPACES. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2014;9(1):71-80. Available from: https://sid.ir/paper/310370/en

IEEE: Copy

ASSADOLLAH NIKNAM, SAEEDEH SHAMSI GAMCHI, and MOHAMMAD JANFADA, “SOME RESULTS ON TVS-CONE NORMED SPACES AND ALGEBRAIC CONE METRIC SPACES,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 9, no. 1, pp. 71–80, 2014, [Online]. Available: https://sid.ir/paper/310370/en

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