Preprint Article Version 1 This version is not peer-reviewed

New Definitons about AI-Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences

Version 1 : Received: 19 February 2018 / Approved: 20 February 2018 / Online: 20 February 2018 (09:15:49 CET)

A peer-reviewed article of this Preprint also exists.

Ki̇şi̇, Ö.; Gümüş, H.; Savas, E. New Definitons about AI-Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences. Axioms 2018, 7, 24. Ki̇şi̇, Ö.; Gümüş, H.; Savas, E. New Definitons about AI-Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences. Axioms 2018, 7, 24.

Journal reference: Axioms 2018, 7, 24
DOI: 10.3390/axioms7020024

Abstract

In this paper, we generalize the concept of I-statistical convergence, which is a recently introduced summability method, with an infinite matrix of complex numbers and a modulus function. Lacunary sequences will also be included in our definitions. The name of our new method will be A^{I}-lacunary statistical convergence with respect to a sequence of modulus functions. We also define strongly A^{I}-lacunary convergence and we give some inclusion relations between these methods.

Subject Areas

Lacunary sequence; ideal convergence; modulus function

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