Some Inequalities in 2-Inner Product Spaces

Cho, Yeol Je; Dragomir, Sever S; White, Albert; Kim, Seong-Sik

doi:10.1515/dema-1999-0304

Cited by 5 publications

(6 citation statements)

References 6 publications

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“…Cho, Y. J. et al [3] and Dragomir, S. S., et al [9] have studied the inequahties of 2-inner product spaces and obtained some related results. 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%

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

confidence: 99%

“…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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“…Y. J. Cho, S. S. Dragomir, A. White and S. S. Kim [5] are presented some inequalities in 2-inner product spaces. Some results on 2-inner product spaces are described by H. Mazaherl and R. Kazemi [6].…”

Section: Introductionmentioning

confidence: 99%

Tensor Product of 2-Frames in 2-Hilbert Spaces

Reddy¹

2016

APM

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“…Note that the concept of 2-Banach space was introduced by Gähler [2]. Later, the various aspect of this concept have been studied in [3,4,5,6,7,8,9]. In particular, Mohammed and Siddique [1] proved analog of some known results of the usual Banach algebras in 2-Banach algebras.…”

Section: Introductionmentioning

confidence: 99%

“…Following by Mohammed and Siddiqui [1], note that a 2-Banach algebra B is an algebra with dim B > 2 which is a 2-Banach space (with respect to 2-norm topology) and in addition, the following condition being satisfied:Note that the concept of 2-Banach space was introduced by Gähler [2]. Later, the various aspect of this concept have been studied in [3,4,5,6,7,8,9]. In particular, Mohammed and Siddique [1] proved analog of some known results of the usual Banach algebras in 2-Banach algebras.Before giving our results, let us give some necessary definitions and notations.…”

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confidence: 99%

SOME RESULTS ON 2-BANACH ALGEBRAS Vol. 4(1) Jan. 2016, No. 2, pp. 11-14 R. TAPDIGOGLU U. KOSEM

2016

Electronic Journal of Mathematical Analysis and Applications

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We consider a 2-Banach algebra and prove some new results, including Gelfand-Mazur type theorems. IntroductionIn this article we give some new results for 2-Banach algebras. In particular, we prove an analogy of famous Gelfand-Mazur theorem for 2-Banach algebras.Recall that the concept of 2-Banach algebra, apparently, was introduced by Mohammed and Siddiqui [1]. Following by Mohammed and Siddiqui [1], note that a 2-Banach algebra B is an algebra with dim B > 2 which is a 2-Banach space (with respect to 2-norm topology) and in addition, the following condition being satisfied:Note that the concept of 2-Banach space was introduced by Gähler [2]. Later, the various aspect of this concept have been studied in [3,4,5,6,7,8,9]. In particular, Mohammed and Siddique [1] proved analog of some known results of the usual Banach algebras in 2-Banach algebras.Before giving our results, let us give some necessary definitions and notations. Let X be a vector space of dimension greater than 1 and ∥., .∥ be a real function on X × X satisfying the following conditions:1) ∥a, b∥ = 0 if and only if a and b are linearly dependent; 2) ∥a, b∥ = ∥b, a∥ ; 3) ∥λa, b∥ = |λ| . ∥a, b∥ for any number λ ; 4) ∥a + b, c∥ ≤ ∥a, c∥ + ∥b, c∥ for every a, b, c ∈ X. ∥., .∥ is called a 2-norm and X equipped with ∥., .∥ is a 2-normed space (see [2]). Gähler [2] has proved that ∥., .∥ is a non-negative function.A sequence {x n } in 2-Banach space X is called a Cauchy sequence if there exists y, z ∈ X such that y and z are linearly independent, the lim ∥x n − x m , y∥ = 0 and 2010 Mathematics Subject Classification. 46J15.

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Some Inequalities in 2-Inner Product Spaces

Abstract: In this paper we extend some results on the refinement of Cauchy-Buniakowski-Schwarz's inequality and Aćzel's inequality in inner product spaces to 2−inner product spaces.

Cited by 5 publications

References 6 publications

Apollonious Identity in Linear 2-Normed Spaces

Apollonious Identity in Linear 2-Normed Spaces

Tensor Product of 2-Frames in 2-Hilbert Spaces

SOME RESULTS ON 2-BANACH ALGEBRAS Vol. 4(1) Jan. 2016, No. 2, pp. 11-14 R. TAPDIGOGLU U. KOSEM

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