Relative uniform convergence of p-absolutely summable sequence of functions
DOI:
https://doi.org/10.5269/bspm.63068Resumo
In this article we introduce the notion of relative uniform convergence of p-absolutely summable sequence of functions. We have investigated its different properties such as solidness, symmetric, convergence-free, monotonic etc. We have established some inclusion relations involving this sequence space.
Referências
[1] E. W. Chittenden, On the limit functions of sequences of continuous functions converging relatively uniformly, Trans. Amer. Math. Soc., vol.20, pp.179–184, 1919.
[2] K. Demirci, A. Boccuto , S. Yıldız, F. Dirik, Relative uniform convergence of a sequence of functions at a point and Korovkin-type approximation theorems, Positivity, vol.24, no.10, pp.1–11, 2020.
[3] K. Demirci, S. Orhan, Statistically relatively uniform convergence of positive linear operators, Results Math., vol.69, pp.359-367, 2016.
[4] K. R. Devi and B. C. Tripathy, Relative uniform convergence of difference double sequence of positive linear functions, Ric. di. Math., 2021 https://doi.org/10.1007/s11587-021-00613-0
[5] K. R. Devi and B. C. Tripathy, On relative uniform convergence of difference double sequences of functions, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 2022. https://doi.org/10.1007/s40010-022-00768-x
[6] K. R. Devi and B. C. Tripathy, Relative uniform convergence of difference sequence of positive linear functions, Trans. Razmadze Math. Inst., vol.176, no.1, pp. 1-? (in press), 2022.
Et. Mikail, C. Muhammed , K. Murat, On λ-statistical convergence of order α of sequences of function, J. Inequal. Appl., 204, 0-8, (2013).
7. Et. Mikail, C. Muhammed, K. Murat, On pointwise λ-statistical convergence of order α of sequence of functions, Asian Eur. J. Math., 6(4), 0-8, 2013.
Et. Mikail, P. Y. Lee and B. C. Tripathy, Strongly almost (V, λ)(_r)-summable sequences defined by Orlicz function, Hokkaido Math. Jour. 35, 197-213, 2006.
[7] E. H. Moore, An Introduction to a form of General Analysis, The New Haven Mathematical Colloquium, Yale University Press, New Haven, pp.30, 1910.
C. Muhammed, K Murat and Et. Mikail, On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory Appl., 33, 1-11, 2013.
[8] P. O. Sahin, F. Dirik, Statistical relative uniform convergence of double sequences of positive linear operators, Appl. Math. E-notes, vol.17, pp.207-220, ,2017.
[9] B. C. Tripathy, On a class of difference sequences related to the p-normed space â„“p, Demonstratio Math., vol.34, no.4, pp.867-872, 2003.
[10] B. C. Tripathy and S. Boroghain , On a class of n-Normed Sequences Related to the â„“p-Space, Bol. Soc. Paran. Mat., vol.31, no.1, pp.167-174, 2004.
[2] K. Demirci, A. Boccuto , S. Yıldız, F. Dirik, Relative uniform convergence of a sequence of functions at a point and Korovkin-type approximation theorems, Positivity, vol.24, no.10, pp.1–11, 2020.
[3] K. Demirci, S. Orhan, Statistically relatively uniform convergence of positive linear operators, Results Math., vol.69, pp.359-367, 2016.
[4] K. R. Devi and B. C. Tripathy, Relative uniform convergence of difference double sequence of positive linear functions, Ric. di. Math., 2021 https://doi.org/10.1007/s11587-021-00613-0
[5] K. R. Devi and B. C. Tripathy, On relative uniform convergence of difference double sequences of functions, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 2022. https://doi.org/10.1007/s40010-022-00768-x
[6] K. R. Devi and B. C. Tripathy, Relative uniform convergence of difference sequence of positive linear functions, Trans. Razmadze Math. Inst., vol.176, no.1, pp. 1-? (in press), 2022.
Et. Mikail, C. Muhammed , K. Murat, On λ-statistical convergence of order α of sequences of function, J. Inequal. Appl., 204, 0-8, (2013).
7. Et. Mikail, C. Muhammed, K. Murat, On pointwise λ-statistical convergence of order α of sequence of functions, Asian Eur. J. Math., 6(4), 0-8, 2013.
Et. Mikail, P. Y. Lee and B. C. Tripathy, Strongly almost (V, λ)(_r)-summable sequences defined by Orlicz function, Hokkaido Math. Jour. 35, 197-213, 2006.
[7] E. H. Moore, An Introduction to a form of General Analysis, The New Haven Mathematical Colloquium, Yale University Press, New Haven, pp.30, 1910.
C. Muhammed, K Murat and Et. Mikail, On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory Appl., 33, 1-11, 2013.
[8] P. O. Sahin, F. Dirik, Statistical relative uniform convergence of double sequences of positive linear operators, Appl. Math. E-notes, vol.17, pp.207-220, ,2017.
[9] B. C. Tripathy, On a class of difference sequences related to the p-normed space â„“p, Demonstratio Math., vol.34, no.4, pp.867-872, 2003.
[10] B. C. Tripathy and S. Boroghain , On a class of n-Normed Sequences Related to the â„“p-Space, Bol. Soc. Paran. Mat., vol.31, no.1, pp.167-174, 2004.
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2024-05-07
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