Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON LACUNARY ∆m-STATISTICAL CONVERGENCE IN G-METRIC SPACES

  • Asif Hussain Jan (Department of Mathematics, National Institute of Technology) ;
  • Tanweer Jalal (Department of Mathematics, National Institute of Technology)
  • Received : 2023.10.25
  • Accepted : 2024.01.04
  • Published : 2024.03.30
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Abstract

The aim of this research is to describe lacunary ∆m-statistically convergent sequences with respect to metrics on generalised metric spaces (g-metric spaces) and to look into the fundamental characteristics of this statistical form of convergence. Also, the relationship between strong summability and lacunary ∆m-statistical convergence in g-metric space is established at the end.

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References

  1. R.Abazari, Statistical convergence in probabilistic generalized metric spaces wrt strong topology, Journal of Inequalities and Applications 2021 (1) (2021), 1-11. http://doi.org/10.1186/s13660-021-02669-w
  2. R.Abazari, Statistical convergence in g-metric spaces, Filomat 2022 (5) (2022), 1461-1468. http://doi.org/10.2298/FIL2205461A
  3. M.A.Alghamdi and M.Mursaleen, λ-Statistical convergence in paranormed space, Abstract and Applied Analysis, 2013, 1-5, http://doi.org/10.1155/2013/264520
  4. A.Alotaibi, and A.M.Alroqi, Statistical convergence in a paranormed space, Journal of Inequalities and Applications 1 (2012), 1-6, http://doi.org/10.1186/1029-242X-2012-39
  5. I.A.Bhat, L.N.Mishra, V.N.Mishra, C.Tunc, O.Tunc, Precision and efficiency of an interpolation approach to weakly singular integral equations, International Journal of Numerical Methods for Heat and Fluid Flow, 2024. http://doi.org/10.1108/HFF-09-2023-0553
  6. H.Choi, S.Kim and S.Y.Yang, Structure for g-Metric Spaces and Related Fixed Point Theorems, arXiv preprint arXiv:1804.03651, 2018. http://doi.org/10.48550/arXiv.1804.03651
  7. J.Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis 8 (12) (1988), 47-64. https://doi.org/10.1524/anly.1988.8.12.47
  8. J.Connor and J.Kline, On statistical limit points and the consistency of statistical convergence, Journal of Mathematical Analysis and Applications 197 (2) (1996), 392-399. http://doi.org/10.1006/jmaa.1996.0027
  9. O.Duman, M.K.Khan and C.Orhan, A-statistical convergence of approximating operators, Mathematical Inequalities and Applications 6 (2003), 689-700. http://doi.org/10.7153/MIA-06-62
  10. A.El-Sayed Ahmed, S.Omran and A.J.Asad, Fixed Point Theorems in Quaternion-Valued Metric Spaces, Abstract and Applied Analysis, 2014, Article ID 258958, 9 pages, http://doi.org/10.1155/2014/258985
  11. M.Et and R.Colak, On some generalized difference difference sequence spaces, Soochow journal of mathematical 24 (4) (1995), 377-386. http://doi.org/10.1023/A:1004597132128
  12. H.Fast, Sur la convergence statistique, Colloquium Mathematicum 2 (1951), 241-244. http://eudml.org/doc/209960 https://doi.org/10.4064/cm-2-3-4-241-244
  13. J.A.Fridy and M.K.Khan, Tauberian theorems via statistical convergence, Journal of Mathematical Analysis and Applications 228 (1) (1998), 73-95. http://doi.org/10.1006/jmaa.1998.6118
  14. J.A.Fridy and C.Orhan, Lacunary statistical summability, Journal of Mathematical Analysis and Applications 173 (2) (1993), 497-504. http://dx.doi.org/10.1006/JMAA.1993.1082
  15. S.K.Jain, G.Meena, L.Rathour, L.N.Mishra, Results in b-metric spaces endowed with graph and application to differential equations, Journal of Applied Mathematics and Informatics 41 (4) (2023), 883-892. https://doi.org/10.14317/JAMI.2023.883
  16. T.Jalal and I.A.Malik, I-convergent triple fuzzy normed spaces, Asia Pacific Journal of Mathematics 41 (5) (2022), 1093-1109. http://dx.doi.org/10.22199/issn.0717-6279-4867
  17. T.Jalal and I.A.Malik, Some new triple sequence spaces over n-normed space , Proyecciones (Antofagasta) 37 (3) (2018), 547-564. http://dx.doi.org/10.4067/S0716-09172018000300547
  18. T.Jalal and I.A.Malik, I -Convergence of triple difference sequence spaces over n-normed space, Tbilisi Mathematical Journal 11 (4) (2018), 93-102. https://doi.org/10.32513/tbilisi/1546570888
  19. T.Jalal and I.A.Malik, Topological and Algebraic Properties of Triple n-normed Spaces, Proceedings of the fifth international conference on mathematics and computing, Springer Singapore, 2021,187-196.
  20. H.Kizmaz, On certain sequence spaces, Canadian Mathematical Bulletian 24 (2) (1981), 169-176. https://doi.org/10.4153/CMB-1981-027-5
  21. G.Mani, L.N.Mishra, V.N.Mishra, Common fixed point theorems in complex partial b-metric space with an application to integral equations, Advanced Studies: Euro-Tbilisi Mathematical Journal 15 (1) (2022), 129-149. https://doi.org/10.32513/asetmj/19322008209
  22. V.N. Mishra, L.N. Mishra, N. Subramanian, S.A.A. Abdulla, Analytic weighted rough statistical convergence with rate of rough convergence and Voronovskaya theorem of triple difference sequences, Applied Sciences (APPS), 22, 2020, 157-168.
  23. V.N. Mishra, N. Rajagopal, P. Thirunavukkarasu and N. Subramanian, The Generalized difference of d (𝜒3I)of fuzzy real numbers over p-metric spaces defined by Musielak Orlicz function, Caspian Journal of Mathematical Sciences 10 (2) (2021), 244-253.
  24. L.N. Mishra, M. Raiz, L. Rathour, V.N. Mishra, Tauberian theorems for weighted means of double sequences in intuitionistic fuzzy normed spaces, Yugoslav Journal of Operations Research 32 (3) (2022), 377-388. http://dx.doi.org/10.2298/YJOR210915005M
  25. V.N. Mishra, M. Raiz, N. Rao, Dunkl analog of Szasz Schurer Beta bivariate operator, Mathematical Foundation of Computing 6 (4) (2022), 651-669, https://doi.org/10.3934/mfc.2022037
  26. Z.Mustafa and B.Sims, A new approach to generalized metric spaces, Journal of Nonlinear and convex Analysis 7 (2) (2006), 289-297.
  27. V.K. Pathak, L.N. Mishra, V.N. Mishra, On the solvability of a class of nonlinear functional integral equations involving Erdelyi-Kober fractional operator, Math. Meth. Appl. Sci, 2023, 1-13, https://doi.org/10.1002/mma.9322
  28. S.K.Paul, L.N.Mishra, V.N.Mishra, D.Baleanu, Analysis of mixed type nonlinear Volterra-Fredholm integral equations involving the Erdelyi-Kober fractional operator, Journal of King Saud University - Science 35 (10) (2023), 102949. https://doi.org/10.1016/j.jksus.2023.102949
  29. M. Raiz, A. Kumar, V. N. Mishra and N.Rao, Dunkl Analogue of Szasz Schurer Beta Operators and their Approximation Behavior, Mathematical Foundation of Computing 5 (4) (2022), 315. https://doi.org/10.3934/mfc.2022007
  30. D. Rai, N. Subramanian, Vishnu Narayan Mishra, The Generalized difference of ∫ 𝜒2I of fuzzy real numbers over p-metric spaces defined by Musielak Orlicz function, New Trends in Math. Sci 4 (3) (2016), 296-306. https://doi.org/10.20852/ntmsci.2016320385
  31. E.Savas and P.Das, A generalized statistical convergence via ideals, Applied Mathematics Letters 24 (6) (2011), 826-830. https://doi.org/10.1016/j.aml.2010.12.022
  32. H.Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicae 2 (1951), 73-74.
  33. A.Zygmund, Trignometric Series, Cambridge University.Press, Cambridge, 1979. https://doi.org/10.1017/CBO9781316036587