A new notion of orthogonality involving area and length
-
Anirban Kundu
,
Tarapada Bag
Abstract
In this paper, a space called geometric space, involving both the notions of area and length, is introduced in general setting. The interplay, between these two ideas, is studied. As a result, a new notion of orthogonality, called area-length orthogonality or A-L orthogonality, is demonstrated. It is shown that A-L orthogonality coincides with the standard notion of orthogonality for inner product spaces. Finally, it is proved that A-L orthogonality implies Birkhoff orthogonality, but not conversely.
The research of first author is funded by UGC, New Delhi, India under NET-JRF scheme (Sr. No. 2061441028, Ref. No.: 22/06/2014(i)EU-V). The research of second author is partially supported by the Special Assistance Programme (SAP) of UGC, New Delhi, India [Grant NO. F 510/3/DRS-III/ 2015 (SAP-I).
Communicated by Marcus Waurick
Acknowledgement
The authors are grateful to the anonymous reviewers and editors for their valuable suggestions and comments to revise the manuscript in the present form.
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Articles in the same Issue
- Regular papers
- Properties of implication in effect algebras
- On a nonlinear relation for computing the overpartition function
- Six-cycle systems
- Representation of bifinite domains by BF-closure spaces
- L-fuzzy cosets in universal algebras
- Density of sets with missing differences and applications
- Degree of independence of numbers
- A generalization of a result on the sum of element orders of a finite group
- A New fuzzy McShane integrability
- Hankel determinants of second and third order for the class 𝓢 of univalent functions
- Herglotz's theorem for Jacobi-Dunkl positive definite sequences
- Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind
- Existence on solutions of a class of casual differential equations on a time scale
- On a general system of difference equations defined by homogeneous functions
- Jordan amenability of banach algebras
- A new notion of orthogonality involving area and length
- Reeb flow invariant ∗-Ricci operators on trans-Sasakian three-manifolds
- A finite graph is homeomorphic to the Reeb graph of a Morse–Bott function
- On first countable quasitopological homotopy groups
