SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE er(u, p)

doi:10.1016/S0252-9602(12)60120-9

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1513-1528.doi: 10.1016/S0252-9602(12)60120-9

SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r(u, p)

Serkan Demiriz, Celal Çakan

1.Department of Mathematics, Faculty of Arts and Science, Gaziosmanpasa University, 60250-Tokat, Turkey； 2.Faculty of Education, ÍnÖnÜ |University, 44280-Malatya, Turkey

收稿日期:2010-08-23 修回日期:2011-04-28 出版日期:2012-07-20 发布日期:2012-07-20

SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r(u, p)

Serkan Demiriz, Celal Çakan

1.Department of Mathematics, Faculty of Arts and Science, Gaziosmanpasa University, 60250-Tokat, Turkey； 2.Faculty of Education, ÍnÖnÜ|University, 44280-Malatya, Turkey

Received:2010-08-23 Revised:2011-04-28 Online:2012-07-20 Published:2012-07-20

摘要/Abstract

摘要：

In this paper, we introduce the sequence space e^r(u, p) and investigate its some topological and geometrical properties such as basis, α-, β-,γ- duals and the uniform
Opial property.

关键词: paranormed sequence spaces, matrix transformations, Luxemburg norm and uniform Opial property

Abstract:

In this paper, we introduce the sequence space e^r(u, p) and investigate its some topological and geometrical properties such as basis, α-, β-,γ- duals and the uniform
Opial property.

Key words: paranormed sequence spaces, matrix transformations, Luxemburg norm and uniform Opial property

中图分类号:

40A05

Serkan Demiriz, Celal Cakan. SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r(u, p)[J]. 数学物理学报(英文版), 2012, 32(4): 1513-1528.

Serkan Demiriz, Celal Cakan. SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r(u, p)[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1513-1528.

[1] Altay B, Ba¸sar F. On some Euler sequence spaces of non-absolute type. Ukrainian Math J, 1999, 57: 1–17

[2] Altay B, Ba¸sar F. Mursaleen M. On the Euler sequence spaces which include the spaces ?p and ?1 I. Inform Sci, 2006, 10: 1450–1462

[3] Altay B, Ba¸sar F. On the paranormed Riesz sequence spaces of non-absolute type. Southeast Asian Bull Math, 2002, 26: 701–715

[4] Altay B, Ba¸sar F. Some paranormed Riesz sequence spaces of non-absolute type. Southeast Asian Bull Math, 2006, 30: 591–608

[5] Ba¸sar F, Altay B. Matrix mappings on the space bs(p) and its α-, β- and γ- duals. Aligarh Bull Math, 2002, 21(1): 79–91

[6] Ba¸sar F. Infinite matrices and almost boundedness. Boll Un Mat Ital, 1992, 6(7): 395–402

[7] Ba¸sar F, Altay B. On the space of sequences of p-bounded variation and related matrix mappings. Ukrainian Math J, 2003, 55(1): 136–147

[8] Choudhary B, Mishra S K. On K¨othe-Toeplitz duals of certain sequence spaces and their matrix transformations. Indian J Pure Appl Math, 1993, 24(5): 291–301

[9] Cui Y, Hudzik H. On the uniform Opial property in some modular sequence spaces. Funct Approx Comment, 1998, 26: 93–102

[10] Demiriz S, C¸ akan C. On some new paranormed Euler sequence spaces and Euler core. Acta Math Sin, English Series, 2010, 26(7): 1207–1222

[11] Diestel J. Geometry of Banach Spaces. Selected Topics. Berlin: Springer-Verlag, 1975

[12] Grosse-Erdmann K G. Matrix transformations between the sequence spaves of Maddox. J Math Anal Appl, 1993, 180: 223–238

[13] Gossez J P, Lami E D. Some geometric properties related to fixed point theory for nonexpensive mappings. Pacific J Math, 1972, 40: 565–573

[14] Kara E E, ¨Ozt¨urk M, Ba¸sar?r M. Some topological and geometric properties of generalized Euler sequence space. Mathematica Slovaca, 2010, 60(3): 1–14

[15] K?zmaz H. On certain sequence spaces. Canad Math Bull, 1981, 24(2): 169–176

[16] Khamsi M A. On Uniform Opial condition and Uniform Kadec-Klee property in Banach and metric spaces. Nonlinear Anal, 1996, 26(10): 1733–1748

[17] Lascarides C G, Maddox I J. Matrix transformations between some classes of sequences. Proc Camb Phil Soc, 1970, 68: 99–104

[18] Maddox I J. Elements of Functional Analysis. 2nd ed. Cambridge: Cambridge University Press, 1988

[19] Maddox I J. Paranormed sequence spaces generated by infinite matrices. Proc Camb Phios Soc. 1968, 64: 335–340

[20] Maligranda L. Orlicz Spaces and Interpolation. Ponzan: Ins Math, Polish Academy of Sciences, 1989

[21] Malkowsky E. Recent results in the theory of matrix transformations in sequence spaces. Mat Vesnik, 1997, 49(1): 187–196

[22] Mursaleen M, Ba¸sar F, Altay B. On the Euler sequence spaces which include the spaces ?p an ?1 II. Nonlinear Anal, 2006, 65: 707–717

[23] Nakano H. Modulared sequence spaces. Proc Jpn Acad, 1951, 27(2): 508–512

[24] Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull Amer Math Soc, 1967, 73: 591–597

[25] Prus S. Banach spaces with uniform Opial property. Nonlinear Anal, 1992, 18(8): 697–704

[26] Polat H, Ba¸sar F. Some Euler of difference sequences of order m. Acta Math Sci, 2007, 27B (2): 254–266

[27] Simons S. The sequence spaces ?(pv) and m(pv). Proc London Math Soc, 1965, 15(3): 422–436

SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r(u, p)

SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r(u, p)

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