On some new sequence spaces

Yıl 2018, Cilt: 20 Sayı: 3, 154 - 162, 29.10.2018

Ekrem Savaş

https://doi.org/10.25092/baunfbed.487747

Cited By: 1

Öz

In this paper, we investigate some new sequence spaces which arise from the notation of generalized de la Vallée-Poussin means and introduce the spaces of strongly λ- invariant summable sequences which happen to be complete paranormed spaces under certain conditions.

Anahtar Kelimeler

σ- convergence , absolutely lambda- invariant , strongly lambda invariant summability

Bazı yeni dizi uzayları üzerine

Öz

Bu makalede, genelleştirilmiş de la Vallée-Poussin ortalamalarından ortaya çıkan bazı yeni dizi uzayları incelenmiş ve belirli koşullar altında tam paranormlu uzay olan kuvvetli λ-değişmez toplanabilir dizi uzayları tanıtılmıştır.

Anahtar Kelimeler

σ- yakınsama , mutlak lambda- değişmez , güçlü lambda değişmez toplanabilirlik

Kaynakça

• Banach, S., Theorie des Operations Lineaires, (1932).
• Duran, J.P., Infinite matrices and almost convergence, Math. Z., 128, 75-83, (1972).
• Hamilton, H.J. and Hill, J. D., On strong summability, Amer. J. Math., 60, 588-94, (1938).
• Kuttner, B., Note on strong summability, J. London Math. Soc., 21, 118-22, (1946).
• King, J.P., Almost summable sequences, Proc. Amer. Math. Soc., 17, 1219-25, (1966).
• Lorentz, G.G., A contribution to the theory of divergent sequences, Acta Math., 80, 167-190, (1948).
• Maddox, I.J., Spaces of strongly summable sequences, Quart. J. Math. Oxford Ser., (2)18, 345-55, (1967).
• Maddox, I.J., Elements of Functional Analysis, Cambridge University Press, (1970).
• Malkowsky, E. and Savaş, E., Some -sequence spaces defined by a modulus, Archivum Math., 36(3), 219-228, (2000).
• Mursaleen, M., Matrix transformation between some new sequence spaces, Houston J. Math., 9, 505–509, (1993),.
• Mursaleen, M., On some new invariant matrix methods of summability, Q.J. Math., 34, 77-86, (1983).
• Nanda, S., Some sequence spaces and almost convergence, J. Austral. Math. Soc. (Series A), 22, 446-455, (1976).
• Savaş, E., Some sequence spaces involving invariant means, Indian J. Math., 31, (1989).
• Savaş, E., A note on some sequence spaces, Doğa Türk. J. Math., 15, (1991).
• Savaş, E., Invariant means and generalization of a theorem of S. Mishra, Doga Türk. J. Math., 14, (1989).
• Savaş, E., Invariant coregular and conull matrices of operators, Hacettepe Bull. Math. Sci. and Eng., 19, (1990).
• Savaş, E., Infinite matrices and generalized almost convergence, Doga Türk. J. Math., 5(3), 1-10, (1987).
• Saraswat, S.K. and Gupta, S.K., Spaces of strongly -summable sequences, Bull. Cal. Math. Soc., 75, 179-184, (1983).
• Schaefer, P., Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36, 104–110, (1972).