Affiliation:
1. Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, Turkey
2. Department of Mathematics, Gauhati University, Guwahati, India
Abstract
In 1970, Ces?ro sequence spaces was introduced by Shiue. In 1981, K?zmaz
defined difference sequence spaces for ??, c0 and c. Then, in 1983, Orhan
introduced Ces?ro difference sequence spaces. Both works used difference
operator and investigated K?the-Toeplitz duals for the new Banach spaces
they introduced. Later, various authors generalized these new spaces,
especially the one introduced by Orhan. In this study, first we discuss the
fixed point property for these spaces. Then, we recall that Goebel and
Kuczumow showed that there exists a very large class of closed, bounded,
convex subsets in Banach space of absolutely summable scalar sequences, ?1
with fixed point property for nonexpansive mappings. So we consider a Goebel
and Kuczumow analogue result for a K?the-Toeplitz dual of a generalized
Ces?ro difference sequence space. We show that there exists a large class
of closed, bounded and convex subsets of these spaces with fixed point
property for nonexpansive mappings.
Publisher
National Library of Serbia
Reference26 articles.
1. A. Aasma, H. Dutta, P.N. Natarajan, An Introductory Course in Summability Theory, John Wiley & Sons, Inc. Hoboken, USA, 2017.
2. F. Başar, H. Dutta, Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties, Chapman and Hall/CRC, Taylor & Francis Group, Boca Raton, London, New York, 2020
3. H. Dutta, Characterization of certain matrix classes involving generalized difference summability spaces, Appl. Sci. APPS. 11 (2009) 60-67.
4. H. Dutta, B.E. Rhoades, Current Topics in Summability Theory and Applications, Springer, Singapore, 2016.
5. H. Dutta, T. Bilgin, Strongly (Vλ,A,Δn(vm), p)-summable sequence spaces defined by an Orlicz function, Appl. Math. Lett. 24 (2011) 1057-1062.