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Some Applications of Summability Theory

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Current Topics in Summability Theory and Applications

Abstract

In this chapter, we will present some recent development in summability theory and its applications. Concretely, we will discuss some applications of summability theory in sequence spaces define by modulus function, Orlicz function, and summability methods, which are related to statistical convergence and their applications. Also we will discuss topological and geometric properties of the sequence spaces, such as the \((\beta )\)-property, Banach-Saks property, Kadec-Klee property, Opial property, etc. In the next section, some applications of summability theory to Tauberian theorems, both in an ordinary sense and in a statistic sense are discussed. In the last section, we will show some results related to the Tauberian theory characterized by weighted summability methods such as, the generalized de la Vallée-Poussin method, generalized Nörlund-Ces\(\grave{a}\)ro etc.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Prishtina, Avenue Mother Teresa, No=5, Prishtine, 10000, Kosova

    Naim L. Braha

  2. Department of Computer Sciences and Applied Mathematics, College Vizioni per Arsim, Rruga Ahmet Kaciku, Nr=3, Ferizaj, 70000, Kosova

    Naim L. Braha

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  1. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  2. Department of Mathematics, Indiana University, Bloomington, Indiana, USA

    Billy E. Rhoades

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Braha, N.L. (2016). Some Applications of Summability Theory. In: Dutta, H., E. Rhoades, B. (eds) Current Topics in Summability Theory and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-10-0913-6_8

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