Some geometric properties of the non-Newtonian sequence spaces lp
 (N)

Güngör, Ni̇han

doi:10.1515/ms-2017-0382

Cited by 20 publications

(8 citation statements)

References 5 publications

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“…For more on the α-arithmetic, its generalized real analysis, its fundamental topological properties related to non-Newtonian metric spaces and its calculus, including non-Newtonian differential equations and its applications, see [7,33,[44][45][46][47][48]. For gentle, thorough and modern introduction to the subject of non-Newtonian calculi, we also refer the reader to the recent book [49].…”

Section: Integralsmentioning

confidence: 99%

On a Non-Newtonian Calculus of Variations

Torres

2021

Axioms

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The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals. Finding the solution of such problems leads to solving the associated Euler–Lagrange equations. The subject has found many applications over the centuries, e.g., in physics, economics, engineering and biology. Up to this moment, however, the theory of the calculus of variations has been confined to Newton’s approach to calculus. As in many applications negative values of admissible functions are not physically plausible, we propose here to develop an alternative calculus of variations based on the non-Newtonian approach first introduced by Grossman and Katz in the period between 1967 and 1970, which provides a calculus defined, from the very beginning, for positive real numbers only, and it is based on a (non-Newtonian) derivative that permits one to compare relative changes between a dependent positive variable and an independent variable that is also positive. In this way, the non-Newtonian calculus of variations we introduce here provides a natural framework for problems involving functions with positive images. Our main result is a first-order optimality condition of Euler–Lagrange type. The new calculus of variations complements the standard one in a nontrivial/multiplicative way, guaranteeing that the solution remains in the physically admissible positive range. An illustrative example is given.

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Section: Integralsmentioning

confidence: 99%

On a Non-Newtonian Calculus of Variations

Torres

2021

Axioms

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“…ağırlıklı Lebesgue uzayının bazı geometrik özelliklerini (Oğur 2018) ve Newtonyen olmayan dizi uzayının bazı geometrik özeliklerini ele alınmıştır (Güngör 2020).…”

Section: Introductionunclassified

Geometrik hesap tarzına göre Lebesgue dizi uzaylarının bazı geometrik özellikleri

DUYAR¹,

EYÜPOĞLU²

2022

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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“…Duyar and Erdogan [7] worked on non-Newtonian real number series. Also, Güngör [11] studied on some geometric properties of p (N ).…”

Section: Introductionmentioning

confidence: 99%

ON -BOUNDEDNESS AND -LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)

Erdogan

DUYAR

2021

Journal of Universal Mathematics

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Many investigations have been made about of non-Newtonian calculus and superposition operators until today. Non-Newtonian superposition operator was defined by Sagır and Erdogan in [9]. In this study, we have defined *-boundedness and *-locally boundedness of operator. We have proved that the non-Newtonian superposition operator N P f : c 0,α → 1,β is *-locally bounded if and only if f satisfies the condition (N A 2 ). Then we have shown that the necessary and sufficient conditions for the *-boundedness of N P f : c 0,α → 1,β . Finally, the similar results have been also obtained for N P f : cα → 1,β .

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Some geometric properties of the non-Newtonian sequence spaces l_p (N)

Cited by 20 publications

References 5 publications

On a Non-Newtonian Calculus of Variations

On a Non-Newtonian Calculus of Variations

Geometrik hesap tarzına göre Lebesgue dizi uzaylarının bazı geometrik özellikleri

ON -BOUNDEDNESS AND -LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)

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Some geometric properties of the non-Newtonian sequence spaces lp (N)

Cited by 20 publications

References 5 publications

On a Non-Newtonian Calculus of Variations

On a Non-Newtonian Calculus of Variations

Geometrik hesap tarzına göre Lebesgue dizi uzaylarının bazı geometrik özellikleri

ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)

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Some geometric properties of the non-Newtonian sequence spaces l_p (N)

ON -BOUNDEDNESS AND -LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)