Volume 7 | Number 1 | Year 2014 | Article Id. IJMTT-V7P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V7P504
In this study we present the functions of bounded kφ-variation of two variables in the sense of Riesz-Korenblum. Moreover we proved that the class of two variables functions of bounded〖kφ〗^*-variation from σ into B is a Banach space and defined an extension E_f on (σ,B), where σ=σ1×σ2,σ1,σ2 are non-empty compact subsets of R.
[1] A. K. Choudhary, S. M. Nengem. (2014). On the Banach Algebra Norm for the Functions of Bounded kφ-variation in the sense of Riesz-Korenblum, IOSR Journal of Mathematics, Vol. 9 Issue 4, pp 07-12.
[2] Castillo M., Rivas S., Sonaja M., Zea I. (2013). “functions of bounded kφ-variationin the sense of Riesz-Korenblum”, Hindawi publishing corporation, Journal of function spaces and applications, Vol. 2013, Article 718507.
[3] Hormozi M. A. A. Ledari& F. Prus - Wisniowki (2011). On Λ– p – Bounded Variation, Bulletin of the Iranian Mathematical Society, Vol. 37 No. 4, pp35-49.
[4] Jordan Camille. (1881). “Sur la serie de Fourier”, Camptesrendushebdomadaires des séances de l’Academie des sciences 92:228-230.
[5] Korenblum B. (1975). “An extension of Nevanlinna theory”, Actamathematica, Vol. 135, No. 3-4, pp. 187-219.
[6] M. Schramm (1985). Functions of φ – Bounded Variation and Riemann – Stieltjes Integration, Transactions of the American Mathematical Society, Volume 287, number 1.
[7] Park J. (2010). “On the functions bounded kφ-variation(I)”, Journal of applied mathematics and informatics, Vol. 28, pp. 487-498.
[8] Riesz F. (1953). “Untersuchugenubersystemeintergrierbarerfunktionen”, mathematischeAnnalen, Vol. 69, No. 4, pp. 115-118.
[9]W. Aziz, H. Leiva, N. Merentes, J. L. Sanches (2010), Functions of two Variables with bounded φ – Variation in the sense of Riesz, Journal of Mathematics and Applications No 32, pp 5-23
[10] Vyas R. G. and K. N. Darji. (2012). “On Banach algebra valued function of Bounded Generalized Variation of one and several variables”, Bulletin of mathematical analysis and applications. ISSN: 1821-1291. Vol. 4 Issue 1, Pages 181-189.
DR. A. K. Choudhary , S. M. Nengem , DR. S. K. Choudhary, "The Banach Algebra Valued Functions of Bounded kφ- Variation of Two Variables in the Sense of Riesz–Korenblum," International Journal of Mathematics Trends and Technology (IJMTT), vol. 7, no. 1, pp. 27-32, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V7P504