Approximative Properties of Diagonal Operators in Orlicz Spaces

REFERENCES

• W. Orlicz (1936). Über Räume (L M ). Bull. Int. Acad. Polon. Sci. A:93–107.
   Google Scholar
• P. B. Djakov and M. S. Ramanujan ( 2000 ). Multipliers between Orlicz Sequence Spaces . Turk. J. Math. 24 : 313 – 319 .
   Google Scholar
• W. Orlicz (1932). Über eine gewisse Klasse von Räumen vom Typus B, Bull. Int. Acad. Polon. Sci. A:207–220.
   Google Scholar
• A. Zygmund (1935). Trigonometrical Series, 2nd ed. Cambridge University Press, Cambridge.
   Google Scholar
• W. A. J. Luxemburg ( 1955 ). Banach Functional Spaces . Koninklijke Van Gorcum & Comp , Assen .
   Google Scholar
• J. Lindenstrauss and L. Tzafriri (1977). Classical Banach spaces I. Springer-Verlag, Berlin.
   Google Scholar
• Y. İ. Gribanov ( 1955 ). Nonlinear operators in Orlicz spaces . Kazan. Gos. Univ. Uchen. Zap. 115 : 5 – 13 .
   Google Scholar
• Y. İ. Gribanov ( 1957 ). To the theory of spaces l M . Kazan. Gos. Univ. Uchen. Zap. 117 : 62 – 65 .
   Google Scholar
• J. Lindenstrauss and L. Tzafriri ( 1971 ). On Orlicz sequence spaces . Israel J. Math. 10 : 379 – 390 .
   Web of Science ®Google Scholar
• M. Aiyub ( 2013 ). On some seminormed sequence spaces defined by Orlicz function . Proyecciones J. Math. 32 : 267 – 280 .
   Google Scholar
• A. I. Stepanets ( 2001 ). Approximation characteristics of the spaces in different metrics . Ukr. Math. J. 53 : 1340 – 1374 .
   Google Scholar
• A. I. Stepanets ( 2001 ). Approximation characteristics of spaces . Ukr. Math. J. 53 : 446 – 475 .
   Google Scholar
• A. I. Stepanets ( 2006 ). Problems of approximation theory in linear spaces . Ukr. Math. J. 58 : 47 – 92 .
   Google Scholar
• F. Gao ( 2010 ). Exact value of the n-term approximation of a diagonal operator . J. Approx. Theory 162 : 646 – 652 .
   Web of Science ®Google Scholar
• V. M. Tikhomirov (1976). Some Problems in Approximation Theory. Moscow State University, Moscow.
   Google Scholar
• A.I. Stepanets (2005). Methods of Approximation Theory. VSP, Leiden, The Netherlands.
   Google Scholar
• A. Pinkus (1985). n-widths in Approximation Theory. Springer–Verlag, Berlin.
   Google Scholar
• S. B. Stechkin ( 1955 ). On the absolute convergence of orthogonal series . Dokl. Akad. Nauk SSSR. 102 : 37 – 40 .
   Google Scholar
• A. I. Stepanets and A. L. Shydlich ( 2005 ). On one extremal problem for positive series . Ukr. Mat. Zh. 57 : 1677 – 1683 .
   Google Scholar
• A. L. Shidlich and S. O. Chaichenko ( 2014 ). On some inequalities of Chebyshev type . Math. Ineq. & Appl. 18 : 1313 – 1320 .
   Google Scholar
• A. L. Shidlich and S. O. Chaichenko (2014). On some inequalities of Chebyshev type. arXiv preprint, arXiv:1405.1256.
   Google Scholar
• G. H. Hardy, J. E. Littlewood, and G. Pólya (1934). Inequalities. Cambridge University Press, Cambridge.
   Google Scholar