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\(\lambda _{d}\)-Statistical Convergence, \(\lambda _{d}\)-statistical Boundedness and Strong \(\left( V,\lambda \right) _{d}-\)summability in Metric Spaces

  • Emine Kayan
  • Rifat ÇolakEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 655)

Abstract

In this paper, we introduce and study \(\lambda _{d} -\)statistical convergence, \(\lambda _{d}-\)statistical boundedness and strong \(\left( V,\lambda \right) _{d}-\)summability of sequences in metric spaces. Furthermore we establish some relations between the sets of \(\lambda _{d} \)-statistically convergent sequences, between the sets of \(\lambda _{d} \)-statistically bounded sequences, between the sets of \(\lambda _{d} -\)statistical convergent sequences and the sets of strongly \(\left( V,\lambda \right) _{d}-\)summable sequences for various sequences \(\lambda =\left( \lambda _{n}\right) \) in \(\varLambda .\) Furthermore we establish some inclusion relations between the sets of strongly \(\left( V,\lambda \right) _{d}-\)summable sequences for various sequences \(\lambda =\left( \lambda _{n}\right) \) in set \(\varLambda ^{*}\).

Keywords

\(\lambda -\)density Statistical convergence \(\lambda -\)statistical convergence Strong summability 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Institute of Science and TechnologyFirat UniversityElazığTurkey
  2. 2.Department of MathematicsFaculty of Science Firat UniversityElazığTurkey

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