New Banach Sequence Spaces That Is Defined By The Aid Of Lucas Numbers

Year 2017, Volume: 7 Issue: 4, 103 - 111, 31.12.2017

Murat Karakaş , Ayşe Metin Karakaş

Abstract

In this work, we establish a new matrix by using Lucas numbers and define a new sequence space.

Besides, we give some inclusion relations and investigate the geometrical properties such as Banach-Saks type ,

weak fixed point property for this space.

Keywords

Banach-Saks property , difference matrix , difference sequence spaces , lucas numbers , weak fixed point property

Lucas Sayıları Yardımıyla Tanımlanan Yeni Banach Dizi Uzayları

Abstract

Bu makalede, Lucas sayılarını kullanarak yeni bir matris oluşturuyoruz ve yeni bir dizi uzayı tanımlıyoruz.

Ayrıca bu uzay için bazı kapsama bağıntıları veriyoruz ve uzayın p tipi Banach-Saks, zayıf sabit nokta gibi

geometrik özelliklerini araştırıyoruz.

Keywords

Banach-Saks özelliği , fark matrisi , fark dizi uzayları , lucas sayıları , zayıf sabit nokta özelliği

References

• Altay B, Başar F, Mursaleen M, 2006. On the Euler sequence spaces which include the spaces l_p and l_∞ I, Inform. Sci, 176: 1450-1462.
• Altay B, Başar F, 2005. Some Euler sequence spaces of nonabsolute type. Ukrainian Math. J, 57: 1-17.
• Altay B, Başar F, 2007. The fine spectrum and the matrix domain of the difference operator Δ on the sequence space l_p, (0<p<1). Commun. Math. Anal., 2: 1-11.
• Başar F, Altay B, 2003. On the space of sequences of p-bounded variation and related matrix mappings. Ukrainian Math. J, 55: 136-147.
• Çolak R, Et M, Malkowsky E, 2004. Some topics of sequence spaces, Lecture notes in Mathematics. Fırat Univ. Press, 1-63.
• Et M, 1993. On some difference sequence spaces. Doğa Mat., 17: 18-24.
• Et M, Esi A, 2000. On Köthe-Toeplitz duals of generalized difference sequence spaces. Bull. Malays. Math. Sci. Soc. (2), 23: 25-32.
• Et M, Çolak R, 1995. On some generalized difference sequence spaces. Soochow J. Math., 21: 377-386.
• Et M, Başarır M, 1997. On some new generalized difference sequence spaces. Period. Math. Hungar., 35: 169-175.
• Et M, Karakaya V, 2014. A new difference sequence set of order α and its geometrical properties. Abstr. Appl. Anal., Art. ID 278907: 4 p.
• García-Falset J, 1994. Stability and fixed points for nonexpansive mappings. Houston J. Math., 20: 495-506.
• Karakaya V, Altun F, 2014. On some geometric properties of a new paranormed sequence space. J. Funct. Spaces, Art. ID 685382: 8 p.
• Karakaş M, Çınar M, Et M, 2013. Some geometric properties of a new sequence space. J. Comput. Anal. Appl., 15: 23-31.
• Gaur AK, Mursaleen M, 1998. Difference sequence spaces. Internat. J. Math. Math. Sci., 21: 701-706.
• Karakaş M, Et M, Karakaya V, 2013. Some geometric properties of a new difference sequence space involving lacunary sequences. Acta Math. Sci. Ser. B Engl. Ed., 33: 1711-1720.
• Koshy T, 2001. Fibonacci and Lucas Numbers with Applications. John Wiley&Sons, Canada. 672 p.
• Karakaş M, 2015. A new regular matrix defined by Fibonacci numbers and its applications. BEU Journal of Science, 4: 205-210.
• Kara EE, Başarır M, 2012. An application of Fibonacci numbers into infinite Toeplitz matrices. Caspian Journal of Mathematics Sciences, 1: 1-6.
• Kızmaz H, 1981. On certain sequence spaces. Canad. Math. Bull., 24: 169-176.
• Kara EE, 2013. Some topological and geometrical properties of new Banach sequence spaces. J. Inequal. Appl., 38: 15 pp.
• Mursaleen M, Çolak R, Et M, 2007. Some geometric inequalities in a new Banach sequence space. J. Inequal. Appl., Art. ID 86757: 6 p.
• Mursaleen M, Noman AK, 2011. On some new sequence spaces of non-absolute type related to the spaces l_p and l_∞ I. Filomat, 25: 33-51.
• Mursaleen M, Noman AK, 2010. On the spaces of λ-convergent and bounded sequences. Thai J. Math., 8: 311-329.
• Mursaleen M, Noman AK, 2010. On some new difference sequence spaces of non-absolute type. Math. Comput. Modelling, 52: 603-617.
• Mursaleen M, Başar F, Altay B, 2006. On the Euler sequence spaces which include the spaces l_p and l_∞ II. Nonlinear Analysis, 65: 707-717.
• Mursaleen M, 1996. Generalized spaces of difference sequences. J. Math. Anal. Appl., 203: 738-745.
• Savaş E, Karakaya V, Şimşek N, 2009. Some l(p)-type new sequence spaces and their geometric properties. Abstr. Appl. Anal., Art. ID 696971: 12 pp.
• Vajda S, 2008. Fibonacci and Lucas Numbers, and the Golden Section Theory and Applications. Dover Edition, NewYork, USA. 189 p.
• Wilansky A, 1984. Summability Through Functional Analysis. Elseiver Science Publishers BV, Amsterdam, The Netherlands. 317 p.