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WIJSMAN LACUNARY IDEAL INVARIANT CONVERGENCE OF DOUBLE SEQUENCES OF SETS
( Erdinç Dündar ),( Nimet Pancaroğlu Akin ) 호남수학회 2020 호남수학학술지 Vol.42 No.2
In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary I<sub>2</sub>-invariant convergence (I<sup>σθ</sup><sub>W2</sub>), Wijsman lacunary I<sub>2</sub>-invariant convergence (I<sup>σθ</sup><sub>W2</sub>), Wijsman p- strongly lacunary invariant convergence ([W<sub>2</sub>N<sub>σθ</sub>]<sub>p</sub>) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W<sub>2</sub>N<sub>σθ</sub>]<sub>p</sub>, I<sup>σθ</sup><sub>W2</sub> and I<sup>σθ</sup><sub>W2</sub>. Also, we introduce the concepts of I<sup>σθ</sup><sub>W2</sub>-Cauchy double sequence and I<sup>σθ</sup><sub>W2</sub> - Cauchy double sequence of sets.
( Erdinç Dündar ),( Nimet Pancaroğlu Akin ),( Ugur Ulusu ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
In this study, we present some asymptotical invariant and asymptotical lacunary invariant equivalence types for double sequences via ideals using modulus functions and investigate relationships between them.
ROUGH STATISTICAL CONVERGENCE IN 2-NORMED SPACES
( MUKADDES ARSLAN ),( Erdinç Dündar ) 호남수학회 2021 호남수학학술지 Vol.43 No.3
In this study, we introduced the notions of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained statistical convergence criteria associated with this set in 2-normed space. Then, we proved that this set is closed and convex in 2-normed space. Also, we examined the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence in 2-normed space.
INVARIANT CONVERGENCE IN FUZZY NORMED SPACES
( ŞEYMA YALVAÇ ),( Erdinç Dündar ) 호남수학회 2021 호남수학학술지 Vol.43 No.3
In this study, we defined the notions of invariant convergence and invariant Cauchy sequences in fuzzy normed spaces. Also, we inves-tigated some properties of invariant convergence and relations between invariant convergence and invariant Cauchy sequences in fuzzy normed spaces.
DEFERRED STRONGLY CESÀRO SUMMABLE AND STATISTICALLY CONVERGENT FUNCTIONS
( Fatih Nuray ),( Erdinç Dündar ),( Uğur Ulusu ) 호남수학회 2022 호남수학학술지 Vol.44 No.4
In this paper, firstly we introduce the concepts of deferred Cesàro summable and deferred statistically convergent function, and secondly we introduce the concepts of deferred almost summable and deferred almost statistically convergent functions. Furthermore, we investigate the relations between these concepts.