On characterization of boundedness of superposition operators on the Maddox space C_r0 (p) of double sequences

Year 2017, Volume: 5 Issue: 4, 80 - 88, 01.10.2017

Oguz Ogur

Abstract

Keywords

Superposition operators, local boundedness, boundedness

References

• Apostol T., M., Mathematical Analysis, Pearson Education Asia Limited and Chine Machine Press, 1974.
• Başar F., Sever Y., The Space of Double Sequences, Math. J. Okayama Univ., 51 (2009), 149-157.
• Başar F., Summability Theory and Its Applications, Bentham Science Publisher, e-books, Monographs, İstanbul (2002)
• Chew T. S., Lee P., Y., Orthoganally Additive Functionals on Sequence Spaces, SEA Bull. Math., 9 (1985), 81-85.
• Dedagich F., Zabreiko P. P., Operator Superpositions in the Space l_p, Sibirskii Matematicheskii Zhurnal, 28 (1987), 86-98.
• Herawaty E., The Locally Boundedness Criteria for Superposition Operators on l_Φ (L), Applied Mathematical Science, 7 (2013), 727-733.
• Moricz, F., Extension Of The Spaces c and c_0 From Single To Double Sequences, Acta Math. Hung., 57 (1–2) (1991), 129–136.
• Kolk,E., Raidjoe, A., The Continuity Of Superposition Operators On Some Sequence Spaces Defined By Moduli, Czechoslovak Mathematical Journal, 57 (2007), 777-792.
• Limaye B.V., Zelstser M., On The Pringsheim Convergence Of Double Series, Proc. Eston. Aca. Sci., 58,2 (2009), 108-121.
• Petranuarat S., Kemprasit Y., Superposition Operators On l_p And c_0 Into l_q (1≤p,q<∞), Southeast Asian Bulletion of Mathematics, 21 (1997), 139-147.
• Pluciennik, R. ,Continuity Of Superposition Operators On w_0 And W_0, Comment. Math. Univ. Carolinae 31(1990), 529-542.
• Pringsheim A., Zur Theorie de Zweifach Unendlichen Zahlenfolgen, Math. Ann., 53 (1900), 289-321.
• Sağır B., Güngör N., Continuity Of Superposition Operators On The Double Sequence SpacesnL_p, Filomat, 29:9 (2015), 2107-2118.
• Sağır B., Güngör N., Locally Boundedness And Continuity Of Superposition Operators On The Double Sequence Spaces C_r0, J. Computational Analysis And Applications, Vol 19, 2 (2015), 365-377.
• Sağır B., Güngör N., Continuity Of Superposition Operators On The Double Sequence Spaces Of Maddox C_r0 (p), Romanian Journal of Mathematics and Computer Science, Vol 5, 1 (2015), 35-45.
• Sama-ae, A., Boundedness Of Superposition Operators On The Sequence Spaces Of Maddoxâ, Master Thesis, Chiang Mai University, 1997
• Sama-ae, A., Boundedness And Continuity Of Superposition Operator On E_r (p) and F_r (p), Songklanakarin J. Sci. Technol., 24 (2002), 452-466.
• Streit, R. F., The Summation Of Convergent Double Series, Texas Tech University (1972).