Some triple difference rough Cesàro and lacunary statistical sequence spaces

• Autorzy: Esi A. , Subramanian N.

Identyfikatory

DOI

10.7862/rf.2018.7

• Języki publikacji: EN

Abstrakty

EN

We generalized the concepts in probability of rough Cesàro and lacunary statistical by introducing the difference operator Δ[αγ] of fractional order, where α is a proper fraction and γ = (γmnk) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence θ and arbitrary sequence p = (prst) of strictly positive real numbers and investigate the topological structures of related with triple difference sequence spaces. The main focus of the present paper is to generalized rough Cesaro and lacunary statistical of triple difference sequence spaces and investigate their topological structures as well as some inclusion concerning the operator Δ[αγ].

Słowa kluczowe

EN

analytic sequence; Musielak-Orlicz function; triple sequences; Chi sequence; Cesàro summable; lacunary statistical convergence

PL

sekwencja analityczna; funkcja Musielaka-Orlicza; sekwencje potrójne; sekwencja Chi; sumowalność metodą Cesàro; konwergencja statystyczna

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2018
• Tom: Vol. 41
• Strony: 81--93
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Esi A.

• Department of Mathematics, Adiyaman University, 02040 Adiyaman, Turkey

autor

Subramanian N.

• Department of Mathematics, SASTRA University, Thanjavur-613 401, India

Bibliografia

• [1] A. Esi, On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews: Discrete Mathematical Structures 1 (2) (2014) 16-25.
• [2] A. Esi, M. Necdet Catalbas, Almost convergence of triple sequences, Global Journal of Mathematical Analysis 2 (1) (2014) 6-10.
• [3] A. Esi, E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. and Inf. Sci. 9 (5) (2015) 2529-2534.
• [4] A.J. Dutta, A. Esi, B.C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis 4 (2) (2013) 16-22.
• [5] S. Debnath, B. Sarma, B.C. Das, Some generalized triple sequence spaces of real numbers, Journal of Nonlinear Analysis and Optimization 6 (1) (2015) 71-79.
• [6] H. Kizmaz, On certain sequence spaces, Canadian Mathematical Bulletin 24 (2) (1981) 169-176.
• [7] P.K. Kamthan, M. Gupta, Sequence Spaces and Series, Lecture Notes, Pure and Applied Mathematics, 65 Marcel Dekker Inc. New York, 1981.
• [8] J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10 (1971) 379-390.
• [9] J. Musielak, Orlicz Spaces, Lectures Notes in Math., 1034, Springer-Verlag, 1983.
• [10] A. Sahiner, M. Gurdal, F.K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math. 8 (2) (2007) 49-55.
• [11] A. Sahiner, B.C. Tripathy, Some I-related properties of triple sequences, Selcuk J. Appl. Math. 9 No. (2) (2008) 9-18.
• [12] N. Subramanian, A. Esi, The generalized tripled difference of X³ sequence spaces, Global Journal of Mathematical Analysis 3 (2) (2015) 54-60.
• [13] A. Esi, N. Subramanian, The triple sequence spaces of X³ on rough statistical convergence defined by Musielak Orlicz function of p-metric, Asian Journal of Mathematical Sciences 1 (1) (2017) 19-25.
• [14] N. Subramanian, A. Esi, M.K. Ozdemir, Some new triple intuitionistic sequence spaces of fuzzy numbers defined by Musielak-Orlicz function, J. Assam Acad. Math. 7 (2017) 14-27.
• [15] A. Esi, N. Subramanian, A. Esi, Triple rough statistical convergence of sequence of Bernstein operators, Int. J. Adv. Appl. Sci. 4 (2) (2017) 28-34.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).