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Variations on lacunary statistical quasi cauchy sequences

open access: yes, 2019
In this paper, we introduce a concept of lacunary statistically p-quasi-Cauchyness of a real sequence in the sense that a sequence (?k) is lacunary statistically p-quasi-Cauchy if limr?? 1 hr |{k ? Ir : |?k+p ? ?k | ? ?}| = 0 for each ? > 0. A function f is called lacunary statistically p-ward continuous on a subset A of the set of real numbers R if it
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Lacunary statistical convergence of double sequences

open access: yesMathematical Communications, 2005
\textit{A. R. Freedman}, \textit{J. J. Sember} and \textit{M. Raphael} [Proc. Lond. Math. Soc., III. Ser. 37, 508--520 (1978; Zbl 0424.40008)] presented a definition for lacunary refinement as follows: \(\rho= \{\overline k_r\}\) is called a lacunary refinement of the lacunary sequence \(\theta= \{k_r\}\) if \(\{k_r\}\subseteq\{\overline k_r\}\).
Patterson, R. F., Savaş, E.
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LACUNARY I_Σ-STATISTICAL CONVERGENCE OF COMPLEX UNCERTAIN SEQUENCE

open access: yes, 2019
This study introduces the concepts of lacunary I-sigma-statistical convergence of complex uncertain sequences: lacunary I-sigma-statistical convergence almost surely (S-theta (I-sigma).a.s.), lacunary I-sigma-statistical convergence in measure, lacunary 4-statistical convergence in mean, lacunary I-sigma-statistical convergence in distribution and ...
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Strongly I_2-lacunary convergence and I_2-lacunary cauchy double sequences of sets

open access: yes, 2015
In this paper, we study the concepts of Wijsman strongly I2-lacunary convergence, Wijsman strongly I*_2 -lacunary convergence, Wijsman strongly I2-lacunary Cauchy sequences and Wijsman strongly I*_2 -lacunary Cauchy double sequences of sets and investigate the properties and relationship between them.
Dündar, Erdinç   +2 more
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