Remarks on 2-Inner Products

Gähler, Siegfried; Misiak, Aleksander

doi:10.1515/dema-1984-0309

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{Xy\z + W) = {Xy\z) + (Xy|w) + -[{Zw\x + Y) -{Zw\x-y)]1

Introduction1

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Cited by 2 publications

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“…For further information and required details on 2-inner product spaces and linear 2-normed spaces, look at the references given in ([l]- [3], [6]- [7], [13]- [14], [15], [16], [17]). …”

Section: {Xy\z + W) = {Xy\z) + (Xy|w) + -[{Zw\x + Y) -{Zw\x-y)]mentioning

confidence: 99%

Apollonious Identity in Linear 2-Normed Spaces

Açıkgöz¹,

Karakus²,

Aslan³

et al. 2009

AIP Conference Proceedings

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Small-world topology of functional connectivity in randomly connected dynamical systems Chaos 22, 033107 (2012) The fundamental theorem of calculus for a matroid J. Math. Phys. 53, 063305 (2012) Brownian motions on metric graphs J. Math. Phys. 53, 095206 (2012) Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: Diluted regime Abstract. We shall extend the well known ApoUonious identity in functional analysis to linear 2-normed spaces and prove it in this spaces.

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“…For further information and required details on 2-inner product spaces and linear 2-normed spaces, look at the references given in ([l]- [3], [6]- [7], [13]- [14], [15], [16], [17]). …”

Section: {Xy\z + W) = {Xy\z) + (Xy|w) + -[{Zw\x + Y) -{Zw\x-y)]mentioning

confidence: 99%

Apollonious Identity in Linear 2-Normed Spaces

Açıkgöz¹,

Karakus²,

Aslan³

et al. 2009

AIP Conference Proceedings

View full text Add to dashboard Cite

show abstract

“…is called a 2-inner product and (X, (·, · | ·)) a 2-inner product space ( [3]). These spaces are studied extensively in [1], [2], [4]- [6] and [11]. In [3] it is shown that x, z = (x, x | z) [9], has shown that for any 2−inner product space (X, (·, · | ·)) , x, z = (x, x | z)…”

Section: Introductionmentioning

confidence: 99%