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Axioms 2018, 7(2), 24; https://doi.org/10.3390/axioms7020024

New Definitions about A I -Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences

1
Department of Mathematics, Faculty of Science, Bartin University, Bartin 74100, Turkey
2
Department of Mathematics, Faculty of Eregli Education, Necmettin Erbakan University, Eregli, Konya 42060, Turkey
3
Department of Mathematics, Istanbul Ticaret University, Üsküdar, Istanbul 34840, Turkey
*
Author to whom correspondence should be addressed.
Received: 19 February 2018 / Revised: 3 April 2018 / Accepted: 10 April 2018 / Published: 13 April 2018
(This article belongs to the Special Issue Mathematical Analysis and Applications)
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Abstract

In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I -statistical convergence, which is a recently introduced summability method. The names of our new methods are A I -lacunary statistical convergence and strongly A I -lacunary convergence with respect to a sequence of modulus functions. These spaces are denoted by S θ A I , F and N θ A I , F , respectively. We give some inclusion relations between S A I , F , S θ A I , F and N θ A I , F . We also investigate Cesáro summability for A I and we obtain some basic results between A I -Cesáro summability, strongly A I -Cesáro summability and the spaces mentioned above. View Full-Text
Keywords: lacunary sequence; statistical convergence; ideal convergence; modulus function; I-statistical convergence lacunary sequence; statistical convergence; ideal convergence; modulus function; I-statistical convergence
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kişi, Ö.; Gümüş, H.; Savas, E. New Definitions about A I -Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences. Axioms 2018, 7, 24.

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