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Some Applications of Summability Theory

In: Current Topics in Summability Theory and Applications

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  • Naim L. Braha

    (University of Prishtina, Department of Mathematics and Computer Sciences
    College Vizioni per Arsim, Department of Computer Sciences and Applied Mathematics)

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 $$(\beta )$$ ( β ) -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 $$\grave{a}$$ a ` ro etc.

Suggested Citation

  • Naim L. Braha, 2016. "Some Applications of Summability Theory," Springer Books, in: Hemen Dutta & Billy E. Rhoades (ed.), Current Topics in Summability Theory and Applications, pages 357-411, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-0913-6_8
    DOI: 10.1007/978-981-10-0913-6_8
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