Statistically Riemann integrable and Summable Sequence of Functions via Deferred Cesàro Mean

Bidu Bhusan Jena1, Hemen Dutta2
1Department of Mathematics, Veer Surendra Sai University of Technology, Burla, India
2Department of Mathematics, Gauhati University, Guwahati, India

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Tài liệu tham khảo

Agnew, R.P.: On deferred Cesàro means. Ann. Math. 33, 413–421 (1932)

Al-Salam, W.A.: Operational representations for the Laguerre and other polynomials. Duke Math. J. 31, 127–142 (1964)

Aasma, A., Dutta, H., Natarajan, P.N.: An Introductory Course in Summability Theory. Wiley, Hoboken (2017)

Braha, N.L., Srivastava, H.M., Mohiuddine, S.A.: A Korovkin-type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean. Appl. Math. Comput. 228, 162–169 (2014)

Dutta, H., Das, S.: On variations via statistical convergence. J. Math. Anal. Appl. 472, 133–147 (2019)

Dutta, H., Rhoades, B.E. (eds.): Current Topics in Summability Theory and Applications, 1st edn. Springer, Singapore (2016)

Fast, H.: Sur la convergence statistique. Colloq. Math. 2, 241–244 (1951)

Fridy, J.A., Orhan, C.: Statistical limit superior and limit inferior. Proc. Am. Math. Soc. 125, 3625–3631 (1997)

Jena, B.B., Paikray, S.K., Dutta, H.: On various new concepts of statistical convergence for sequences of random variables via deferred Cesàro mean. J. Math. Anal. Appl. 487, 1–18 (2020). ((Article ID: 123950))

Korovkin, P.P.: Convergence of linear positive operators in the spaces of continuous functions (in Russian). Doklady Akad. Nauk. SSSR (New Ser.) 90, 961–964 (1953)

Srivastava, H.M., Jena, B.B., Paikray, S.K., Misra, U.K.: A certain class of weighted statistical convergence and associated Korovkin type approximation theorems for trigonometric functions. Math. Methods Appl. Sci. 41, 671–683 (2018)

Srivastava, H.M., Jena, B.B., Paikray, S.K., Misra, U.K.: Generalized equi-statistical convergence of the deferred Nörlund summability and its applications to associated approximation theorems. Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (RACSAM) 112, 1487–1501 (2018)

Steinhaus, H.: Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2, 73–74 (1951)

Trench, W.F.: Introduction to Real Analysis. Pearson Education, London (2013)

Viskov, O.V., Srivastava, H.M.: New approaches to certain identities involving differential operators. J. Math. Anal. Appl. 186, 1–10 (1994)