Lacunary Statistical Convergence Sequence in Neutrosophic Metric Space

Authors

  • J. Johnsy Alagappa University,P.G. and Research Department of Mathematics, Raja Doraisingam Government Arts College (affiliated to Alagappa University), Sivagangai, Karaikudi, Tamilnadu, India https://orcid.org/0009-0007-7790-0321
  • M. Jeyaraman P.G. and Research Department of Mathematics, Raja Doraisingam Government Arts College (affiliated to Alagappa University), Sivagangai, Karaikudi, Tamilnadu, India https://orcid.org/0000-0002-0364-1845

DOI:

https://doi.org/10.26713/cma.v14i5.2293

Keywords:

Lacunary sequence, Neutrosophic normed linear space, Wijsman convergence, Cesaro summability, Sequence of sets

Abstract

Researchers describe the theory of Lacunary Strongly Convergence ( LSC ) and its application to sequences of sets in Neutrosophic Metric Spaces(NMS). We derive a conceptual connection between these ideas. In addition, that we have defined certain required and adequate criteria to ensure the similarity for Statistical Convergence(StC ) and Lacunary Statistical Convergence(LStC) sets for the sequence of NMS. We develop certain findings along with the idea of enhanced Cesaro summability in NMS.

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References

K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) (1986), 87 – 96, DOI: 10.1016/S0165-0114(86)80034-3.

H. Fast, Sur la convergence statistique, Colloquium Mathematicae 2(3-4) (1951), 241 – 244, URL: https://eudml.org/doc/209960.

J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific Journal of Mathematics 160(1) (1993), 43 – 51, DOI: 10.2140/pjm.1993.160.43.

J.A. Fridy and C. Orhan, Lacunary statistical summability, Journal of Mathematical Analysis and Applications 173(2) (1993), 497 – 504, DOI: 10.1006/jmaa.1993.1082.

A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64(3) (1994), 395 – 399, DOI: 10.1016/0165-0114(94)90162-7.

A. Gökhan, M. Et and M. Mursaleen, Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers, Mathematical and Computer Modelling 49(3-4) (2009), 548 – 555, DOI: 10.1016/j.mcm.2008.02.006.

C. Granados and A. Dhital, Statistical convergence of double sequences in neutrosophic normed spaces, Neutrosophic Sets and Systems 42 (2021), 333 – 344, DOI: 10.5281/zenodo.4718194.

M. Jeyaraman, H. Aydi and M. De La Sen, New results for multivalued mappings in hausdorff neutrosophic metric spaces, Axioms 11(12) (724), 1 – 14, DOI: 10.3390/axioms11120724.

M. Jeyaraman, A. Ramachandran and V.B. Shakila, Approximate fixed point theorems for weak contractions on neutrosophic normed spaces, Journal of Computational Mathematica 6(1) (2022), 134 – 158, DOI: 10.26524/cm127.

M. Jeyaraman, A.N. Mangayarkkarasi, V. Jeyanthi and R. Pandiselvi, Hyers-Ulam-Rassias stability for functional equation in neutrosophic normed spaces, International Journal of Neutrosophic Science 18(1) (2022), 127 – 143, DOI: 10.54216/IJNS.180111.

O. Ki¸si, I-Lacunary statistical convergence in intuitionistic fuzzy normed spaces, Afyon Kocatepe University Journal of Science and Engineering 20 (2020), 021301, 207 – 212, URL: https://dergipark.org.tr/en/download/article-file/1106964.

F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasciculi Mathematici 49 (2012), 87 – 99, URL: https://fasciculi-mathematici.put.poznan.pl/artykuly/49/FM49(2012)-NurayFRhoadesBE.pdf.

J.H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals 22(5) (2004), 1039 – 1046, DOI: 10.1016/j.chaos.2004.02.051.

R. Saadati and J.H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons & Fractals 27(2) (2006), 331 – 344, DOI: 10.1016/j.chaos.2005.03.019.

S. Sowndrarajan, M. Jeyaraman and F. Smarandache, Fixed point results for contraction theorem in neutrosophic metric spaces, Neutrosophic Sets and Systems 36(1) (2020), Article 23, 308 – 318, URL: https://digitalrepository.unm.edu/nss_journal/vol36/iss1/23/.

U. Ulusu and F. Nuray, Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics 4(2) (2012), 99 – 109, DOI: 10.3968/j.pam.1925252820120402.2264.

R.A. Wijsman, Convergence of sequences of convex sets, cones and functions – II, Transactions of the American Mathematical Society 123(1) (1966), 32 – 45, URL: https://www.ams.org/journals/tran/1966-123-01/.

L.A. Zadeh, Fuzzy sets, Inform and Control 8(3) (1965), 338 – 365, DOI: 10.1016/S0019-9958(65)90241-X.

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Published

16-04-2024
CITATION

How to Cite

Johnsy, J., & Jeyaraman, M. (2024). Lacunary Statistical Convergence Sequence in Neutrosophic Metric Space. Communications in Mathematics and Applications, 14(5), 1493–1506. https://doi.org/10.26713/cma.v14i5.2293

Issue

Vol. 14 No. 5 (2023)

Section

Research Article

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