본문 바로가기
KERD
논문KCI 등재

Density by Moduli and Korovkin Type Approximation Theorem of Boyanov and Veselinov

Vinod K. Bhardwaj|Shweta Dhawan
경북대학교 자연과학대학 수학과|2018.12|Kyungpook Mathematical Journal|제58권 제4호|pp. 733-746

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

statistical convergencemodulus functionrate of convergencepositive linear operatorKorovkin type approximation theorem
주제분류수학

초록

The concept of f-statistical convergence which is, in fact, a generalization of statistical convergence, has been introduced recently by Aizpuru et al. (Quaest. Math. 37: 525-530, 2014). The main object of this paper is to prove an f-statistical analog of the classical Korovkin type approximation theorem of Boyanov and Veselinov. It is shown that the f-statistical analog is intermediate between the classical theorem and its statistical analog. As an application, we estimate the rate of f-statistical convergence of the sequence of positive linear operators defined from C*[0,infinite) into itself.

Abstract

The concept of f-statistical convergence which is, in fact, a generalization of statistical convergence, has been introduced recently by Aizpuru et al. (Quaest. Math. 37: 525-530, 2014). The main object of this paper is to prove an f-statistical analog of the classical Korovkin type approximation theorem of Boyanov and Veselinov. It is shown that the f-statistical analog is intermediate between the classical theorem and its statistical analog. As an application, we estimate the rate of f-statistical convergence of the sequence of positive linear operators defined from C*[0,infinite) into itself.

참고문헌 (36)

  1. A. Aizpuru, "Density by moduli and statistical convergence", Quaest. Math, 37, pp.525~530 (2014)
  2. F. Altomare, "Korovkin-type theorems and approximation by positive linear operators", Surv. Approx. Theory, 5, pp.92~164 (2010)
  3. V. A. Baskakov, "An example of a sequence of linear positive operators in the space of continuous functions", Dokl. Akad. Nauk, 113, pp.249~251 (1957)
  4. C. Belen, "Generalized weighted statistical convergence and application", Appl. Math. Comput, 219(18), pp.9821~9826 (2013)
  5. V. K. Bhardwaj, "f-statistical convergence of order α and strong Cesaro summability of order α with respect to a modulus", J. Inequal. Appl, 2015(332), pp.14~ (2015)
  6. V. K. Bhardwaj, "Density by moduli and lacunary statistical conver-gence", Abstr. Appl. Anal, 2016, pp.11~ (2016)
  7. V. K. Bhardwaj, "Density by moduli and Wijsman lacunary statistical convergence of sequences of sets", J. Inequal. Appl, 25, pp.20~ (2017)
  8. V. K. Bhardwaj, "Korovkin type approximation theorem via f-statistical convergence", J. Math. Anal, 9(2), pp.99~117 (2018)
  9. V. K. Bhardwaj, "Density by moduli and Wijsman statistical convergence", Bull. Belg. Math. Soc. Simon Stevin, 24(3), pp.393~415 (2017)
  10. V. K. Bhardwaj, "Density by moduli and statistical bound-edness", Abstr. Appl. Anal, 2016, pp.6~ (2016)
  11. H. Bohman, "On approximation of continuous and of analytic functions", Ark. Mat, 2, pp.43~56 (1952)
  12. B. D. Boyanov, "A note on the approximation of functions in an infinite interval by linear positive operators", Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.), 14(62), pp.9~1 (1970)
  13. L. N. Braha, "Some weighted equi-statistical convergence and Korovkin type-theorem", Results Math, 70, pp.433~446 (2016)
  14. O. Duman, "Statistical approximation for periodic functions", Demonstratio Math, 36, pp.873~878 (2003)
  15. O. Duman, "Statistical approximation for infinite intervals", ~
  16. H. Fast, "Sur la convergence statistique", Colloquium Math, 2, pp.241~244 (1951)
  17. J. A. Fridy, "On statistical convergence", Analysis, 5, pp.301~313 (1985)
  18. A. D. Gadjiev, "Some approximation theorems via statistical conver-gence", Rocky Mountain J. Math, 32, pp.129~138 (2002)
  19. A. Holhos, "The rate of approximation of functions in an infinite interval by positive linear operators", Stud. Univ. Babes-Bolyai Math, 55(2), pp.133~142 (2010)
  20. A. Holhos, "Contributions to the approximation of functions", Ph. D, pp.2010
  21. U. Kadak, "Statistical weighted B-summability and its applications to approximation theorems", Appl. Math. Comput, 302, pp.80~96 (2017)
  22. E. Kolk, "Statistically convergent sequences in normed spaces, Reports of convergence \Methods of algebra and analysis", Tartu, pp.63~66 (1988)
  23. P. P. Korovkin, "On convergence of linear positive operators in the space of continuous functions", Doklady Akad. Nauk. SSSR(N.S.), 90, pp.961~964 (1953)
  24. P. P. Korovkin, "Linear operators and approximation theory" (1960), Hindustan Publ. Corp
  25. I. J. Maddox, "Sequence spaces defined by a modulus", Math. Proc. Cambridge Philos. Soc, 100, pp.161~166 (1986)
  26. S. A. Mohiuddine, "Statistical weighted A-summability with application to Korovkin's type approximation theorem", J. Inequal. Appl, 2016(101), pp.13~ (2016)
  27. S. A. Mohiuddine, "Statistical summability (C, 1) and a Korovkin type approximation theorem", J. Inequal. Appl, 2012(172), pp.8~ (2012)
  28. M. Mursaleen, "Statistical lacunary summability and Korovkin type approximation theorem", Ann. Univ. Ferrara Sez. VII Sci. Mat, 57, pp.373~381 (2011)
  29. I. Niven, "An introduction to the theory of numbers" (1991), John Willey and Sons
  30. P. A. Pitul, "valuation of the approximation order by positive linear operators", Ph. D, pp.2007
  31. T. Popoviciu, "Asupra demonstratiei teoremei lui Weierstrass cu ajutorul polinoamelor de interpolare", Lucraarile Sesiunii Generale Stiintifice din, pp.1664~1667 (1951), Academiei Republicii Populare Rombane
  32. W. H. Ruckle, "FK spaces in which the sequence of coordinate vectors is bounded", Canad. J. Math, 25, pp.973~978 (1973)
  33. T. Salat, "On statistically convergent sequences of real numbers", Math. Slovaca, 30(2), pp.139~150 (1980)
  34. I. J. Schoenberg, "The integrability of certain functions and related summability meth-ods", Amer. Math. Monthly, 66, pp.361~375 (1959)
  35. H. Steinhaus, "Sur la convergence ordinaire et la convergence asymptotique", Colloq. Math, 2, pp.73~74 (1951)
  36. A. Zygmund, "Trigonometric series" (1979), Camb. Univ. Press

관련 논문AI추천

A KOROVKIN TYPE APPROXIMATION THEOREM FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS OF TWO VARIABLES IN A-STATISTICAL SENSEFadime Dirik, Kamil Demirci대한수학회 · 대한수학회보2010 · 제47권 제4호On statistical approximation properties of modified q-Bernstein-Schurer OperatorsMei-Ying Ren, Xiao-Ming Zeng대한수학회 · 대한수학회보2013 · 제50권 제4호STATISTICAL A-SUMMABILITY OF DOUBLE SEQUENCES AND A KOROVKIN TYPE APPROXIMATION THEOREMCemal Belen, Mohammad Mursaleen, Mustafa Yildirim대한수학회 · 대한수학회보2012 · 제49권 제4호Statistical Approximation of Szasz Type Operators Based on Charlier PolynomialsArun Kajla경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제4호Statistical convergence for General Beta OperatorsMehmet Ali Ozarslan, Naokant Deo, Neha Bhardwaj강원경기수학회 · 한국수학논문집2014 · 제22권 제4호On triple sequence space of Bernstein-Stancu operator of rough $I_{\lambda}% -$statistical convergence of weighted $g\left( A\right) $A. Esi, Ayten Esi, N. Subramanian기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2018 · 제16권 제3호

이 간행물의 다른 논문 (14건)

Preservers of Gershgorin Set of Jordan Product of MatricesSandeep Kanodia, Kilambi Santaram, Manoj Joshi, Kota Nagalakshmi Rajeshwaripp. 589-597On a Generalization of the Pentagonal Number TheoremHo-Hon Leungpp. 599-613Certain Models of the Lie Algebra K5 and Their Connection with Special FunctionsGeeta Rani, Sarasvati Yadavpp. 615-625Regularity of a Particular Subsemigroup of the Semigroup of Transformations Preserving an EquivalenceJittisak Rakbudpp. 627-635On [m,C]-symmetric OperatorsMuneo Cho, Jun Tomiyama, Muneo Cho, K^otar^o Tanahashipp. 637-650
원문 보기