Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces

Yıl 2019, Cilt: 2 Sayı: 4, 293 - 302, 29.12.2019

Vakeel Ahmad Khan , Sameera Aa Abdullah Kamal Mas Alshlool

Öz

In this paper  we  introduce some new sequence spaces $ c_{0}^{I}(\hat{F},p)$, $c^{I}(\hat{F},p)$ and $\ell_{\infty}^{I}(\hat{F},p)$ for  $p=(p_n),$ a sequence of positive real numbers. In addition, we study  some topological and algebraic properties on these spaces. Lastly, we  examine  some inclusion relations on these spaces.

Anahtar Kelimeler

Fibonacci difference matrix, I-Cauchy, I-convergence, Paranormed space

Destekleyen Kurum

aligarh muslim university aligarh india

Proje Numarası

amu231678

Kaynakça

• [1] A. Wilansky, Summability Through Functional Analysis, North-Holland Mathematics Studies, Amsterdam-New York- Oxford, 1984.
• [2] H. Nakano, Modulared sequence spaces, Proc. Japan Acad., 27(9) (1951), 508-512.
• [3] S. Simons, The sequence spaces l(pv) and m(pv), Proc. Lond. Math. Soc., 3(1) (1965), 422-436.
• [4] IJ. Maddox, Spaces of strongly summable sequences, Q. J. Math., 18(1) (1967), 345-355.
• [5] IJ. Maddox, Paranormed sequence spaces generated by infinite matrices, Cambridge University Press, 64 (1968), 335-340.
• [6] H. Ellidokuzo˘glu, S. Demiriz, A. K¨oseo˘glu On the paranormed binomial sequence spaces, Univers. J. Math. Appl., 1(3) (2018), 137-147.
• [7] B. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4) (2009), 485-494.
• [8] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
• [9] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73-74. [10] P. Kostyrko, M. Macaj, T.Salat, Statistical convergence and I–convergence, Real Anal. Exchange, (1999).
• [11] Dems, Katarzyna, On I-Cauchy sequences, Real Anal. Exchange, 30(1) (2004), 123-128.
• [12] K. Vakeel, A. Kamal, A. Sameera, Spaces of ideal convergent sequences of bounded linear operators, Numer. Funct. Anal. Optim., 39(12) (2018), 1278-1290.
• [13] K. Vakeel, R. Rami, A. Kamal. A. Sameera, A. Ayaz, On ideal convergence Fibonacci difference sequence spaces, Adv. Difference Equ., 2018(1) (2018), 199.
• [14] K. Vakeel, R. Rami, A. Kamal. A. Sameera, A. Esi, Some new spaces of ideal convergent double sequences by using compact operator, J. Appl. Sci., 17(9) (2017), 467-474.
• [15] B. Tripathy, B. Hazarika, I-convergent sequence spaces associated with multiplier sequences, Math. Inequal. Appl., 11(3) (2008), 543.
• [16] T. Salat, B. Tripathy, M. Ziman, On I-convergence field, Ital. J. Pure Appl. Math, 17(5) (2005), 1-8.
• [17] E. E. Kara, M. ˙Ilkhan, On some paranormed A-ideal convergent sequence spaces defined by Orlicz function, Asian J. Math. Comput. Research, 4(4) (2015), 183-194.
• [18] M. Basarir, F. Basar, E. E. Kara, On the spaces of Fibonacci difference absolutely p-summable, null and convergent sequences, Sarajevo J. Math., 12(25) (2016), 2.
• [19] M. Candan, K. Kayaduman , Almost convergent sequence space derived by generalized Fibonacci matrix and Fibonacci core, Br. J. Math. Comput. Sci., 7(2) (2015), 150- 167.
• [20] V. Karakaya, E. Savas, H. Polat, Some paranormed Euler sequence spaces of difference sequences of order m, Math. Slovaca, 63(4) (2013), 849-862.
• [21] E. Malkowsky, Recent results in the theory of matrix transformations in sequence spaces, Mathmaticki Vesnik-Beograd, 49 (1997), 187-196.
• [22] M.Mursaleen, On some new sequence spaces of non-absolute type related to the spaces `p and `¥ I, Filomat, 25(2) (2011), 33-51.
• [23] K. Vakeel, A. Kamal, M. Abdullah, A. Sameera, On spaces of ideal convergent Fibonacci difference sequence defined by Orlicz function, Sigma, 37(1) (2019), 143-154.
• [24] E. Kara, M. Demiriz, Some new paranormed difference sequence spaces derived by Fibonacci numbers, Miskolc Math. Notes, 16(2) (2015), 907-923.
• [25] H.Kizmaz, Certain sequence spaces, Can. Math. Bull, 24(2) (1981), 169-176.
• [26] B.Tripathy, A. Esi, A new type of difference sequence spaces, Internat. J. Sci. Tech., 1(1) (2006), 11-14.
• [27] S. Aydın, H. Polat, Difference sequence spaces derived by using Pascal transform, Fundam. J. Math. Appl., 2(1) (2019), 56-62.
• [28] A. Esi, Some classes of generalized difference paranormed sequence spaces associated with multiplier sequences, J. Comput. Anal. Appl., 11(3) (2009).
• [29] A. Esi, B. Tripathy, B. Sarma, On some new type generalized difference sequence spaces, Math. Slovaca, 57(5) (2007), 475-482.
• [30] E. E. Kara, M. ˙Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11) (2016), 2208-2223.
• [31] T. Salat, M. Tripathy, M. Ziman, On some properties of i-convergence, Tatra Mt. Math. Publ, 28(5) (2004), 279-289.
• [32] C. Lascarides, On the equivalence of certain sets of sequences, Indian J. Math., 25(1) (1983), 41-52.
• [33] G. Petersen, Regular Matrix Transformations, McGraw-Hill, 1966.