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DOI :10.26650/ijmath.2023.00001   IUP :10.26650/ijmath.2023.00001    Full Text (PDF)

Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm

Esra Başar, Badik Hüseyin Uysal, Şeyma Yaşar

Let Φ be an Orlicz function and 𝐿 Φ(𝑋, Σ, 𝜇) be the corresponding Orlicz space on a non-atomic, 𝜎-finite, complete measure space (𝑋, Σ, 𝜇). It is known that extreme points which are connected with rotundity of the whole spaces are the most essential and important geometric notion in the geometric theory of Banach spaces. On the other hand, geometric theory of complex Banach spaces has significant applications that differ from the geometric theory of real Banach spaces. In this paper, we first describe the complex extreme points of unit ball of Orlicz spaces equipped with the 𝑠-norm where 𝑠 is a strictly increasing outer function. We also give criteria for complex rotundity. Our study generalizes and unifies the results that have been obtained for the Orlicz norm and the 𝑝-Amemiya norm (1 < 𝑝 < ∞) separately. 

Keywords: Orlicz space, complex extreme points, complex strictly rotund, s-norm

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APA

Başar, E., Uysal, B.H., & Yaşar, Ş. (2023). Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm. Istanbul Journal of Mathematics, 1(1), 40-47. https://doi.org/10.26650/ijmath.2023.00001


AMA

Başar E, Uysal B H, Yaşar Ş. Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm. Istanbul Journal of Mathematics. 2023;1(1):40-47. https://doi.org/10.26650/ijmath.2023.00001


ABNT

Başar, E.; Uysal, B.H.; Yaşar, Ş. Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm. Istanbul Journal of Mathematics, [Publisher Location], v. 1, n. 1, p. 40-47, 2023.


Chicago: Author-Date Style

Başar, Esra, and Badik Hüseyin Uysal and Şeyma Yaşar. 2023. “Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm.” Istanbul Journal of Mathematics 1, no. 1: 40-47. https://doi.org/10.26650/ijmath.2023.00001


Chicago: Humanities Style

Başar, Esra, and Badik Hüseyin Uysal and Şeyma Yaşar. “Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm.” Istanbul Journal of Mathematics 1, no. 1 (Sep. 2023): 40-47. https://doi.org/10.26650/ijmath.2023.00001


Harvard: Australian Style

Başar, E & Uysal, BH & Yaşar, Ş 2023, 'Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm', Istanbul Journal of Mathematics, vol. 1, no. 1, pp. 40-47, viewed 21 Sep. 2023, https://doi.org/10.26650/ijmath.2023.00001


Harvard: Author-Date Style

Başar, E. and Uysal, B.H. and Yaşar, Ş. (2023) ‘Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm’, Istanbul Journal of Mathematics, 1(1), pp. 40-47. https://doi.org/10.26650/ijmath.2023.00001 (21 Sep. 2023).


MLA

Başar, Esra, and Badik Hüseyin Uysal and Şeyma Yaşar. “Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm.” Istanbul Journal of Mathematics, vol. 1, no. 1, 2023, pp. 40-47. [Database Container], https://doi.org/10.26650/ijmath.2023.00001


Vancouver

Başar E, Uysal BH, Yaşar Ş. Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm. Istanbul Journal of Mathematics [Internet]. 21 Sep. 2023 [cited 21 Sep. 2023];1(1):40-47. Available from: https://doi.org/10.26650/ijmath.2023.00001 doi: 10.26650/ijmath.2023.00001


ISNAD

Başar, Esra - Uysal, BadikHüseyin - Yaşar, Şeyma. “Complex extreme points and complex rotundity in Orlicz spaces equipped with the 𝑠-norm”. Istanbul Journal of Mathematics 1/1 (Sep. 2023): 40-47. https://doi.org/10.26650/ijmath.2023.00001



TIMELINE


Submitted17.04.2023
Accepted01.06.2023
Published Online06.06.2023

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