Journal of the Egyptian Mathematical Society, 2016
An ideal I is a family of subsets of N Â N which is closed under taking finite unions and subsets... more An ideal I is a family of subsets of N Â N which is closed under taking finite unions and subsets of its elements. In this article, the concept of lacunary ideal convergence of double sequences has been introduced. Also the relation between lacunary ideal convergent and lacunary Cauchy double sequences has been established. Furthermore, the notions of lacunary ideal limit point and lacunary ideal cluster points have been introduced and find the relation between these two notions. Finally, we have studied the properties such as solidity, monotonic.
This paper presents the following definition, which is a natural combination of the definitions f... more This paper presents the following definition, which is a natural combination of the definitions for asymptotically equivalent, I-statistically limit and I-lacunary statistical convergence. Let θ be a lacunary sequence; the two nonnegative sequences x = (x k ) and y = (y k ) are said to be I-asymptotically lacunary statistical equivalent of multiple L provided that for every > 0, and δ > 0, ∼ y) and simply I-asymptotically lacunary statistical equivalent if L = 1.
In this article we introduce the lacunary difference sequence spaces defined by Musielak–Orlicz f... more In this article we introduce the lacunary difference sequence spaces defined by Musielak–Orlicz functions and study their algebraic and topological properties. Also we obtain some relations related to these spaces.
An ideal I is a family of subsets of positive integers N which is closed under taking finite unio... more An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In this paper, we introduce the concepts of ideal ?-convergence, ideal ?-Cauchy and ideal ?-bounded sequence in locally solid Riesz space endowed with the topology ?. Some basic properties of these concepts has been investigated. We also examine the ideal ?-continuity of a mapping defined on locally solid Riesz space.
Journal of the Egyptian Mathematical Society, 2014
In this article we introduce paranorm ideal convergent sequence spaces using Zweier transform and... more In this article we introduce paranorm ideal convergent sequence spaces using Zweier transform and Orlicz function. We study some topological and algebraic properties. Further we prove some inclusion relations related to these new spaces. MATHEMATICS SUBJECT CLASSIFICATION: 40A05; 40D25; 40G15 ª 2013 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.
We introduce the concept of (λ,μ)-statistical convergence in n-normed spaces, where λ=(λ r ) and ... more We introduce the concept of (λ,μ)-statistical convergence in n-normed spaces, where λ=(λ r ) and μ=(μ s ) are two non-decreasing sequences of positive real numbers, each tending to ∞ and such that λ r+1 ≤λ r +1, λ 1 =1; μ s+1 ≤μ s +1, μ 1 =1. Some inclusion relations between the sets of statistically convergent and (λ,μ)-statistically convergent double sequences are established. We find its relation to statistical convergence, (C,1,1)-summability and strong (V,λ,μ)-summability in n-normed spaces.
In this article we study the noton of I-monotonic sequences. We prove the decomposition theorem a... more In this article we study the noton of I-monotonic sequences. We prove the decomposition theorem and generalize some of the results on monotonic sequences. We also introduce I-convergent series and studied some results.
In this article, we introduce the lacunary generalized difference double paranormed sequence spac... more In this article, we introduce the lacunary generalized difference double paranormed sequence spaces 2
In this article we introduce the sequence spaces ( , M, , p, q, v , ( , M, , p, q, v , and ( , M,... more In this article we introduce the sequence spaces ( , M, , p, q, v , ( , M, , p, q, v , and ( , M, , p, q, v and study their algebraic and topological properties. Also we obtain some inclusion relations. ξ N m Δ 1 ) ξ N m Δ 0 ) ξ N m Δ ∞ )
In this article we introduce the sequence spaces c I (Λ) , c I 0 (Λ) , m I (Λ) and m I 0 (Λ) asso... more In this article we introduce the sequence spaces c I (Λ) , c I 0 (Λ) , m I (Λ) and m I 0 (Λ) associated with the multiplier sequence Λ = (λ k ) of non-zero scalars. We study the different algebraic and topological properties of these sequence spaces like solidness, symmetricity, sequence algebra, convergence free etc. Also we characterize the multiplier problem and obtain some inclusion relation involving these sequence spaces. : 40A05, 40C05.
In this article we introduced the sequence spaces ( ), 0 ( ), ( ) and 0 ( ) for = ( ), a sequence... more In this article we introduced the sequence spaces ( ), 0 ( ), ( ) and 0 ( ) for = ( ), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces. We prove the decomposition theorem and obtain some inclusion relations. c ⃝2009 Mathematical Institute Slovak Academy of Sciences 2000 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 40A05, 46A45. K e y w o r d s: ideal, filter, -convergent, -null, paranorm.
Acta Mathematicae Applicatae Sinica, English Series, 2011
In this article we introduce the sequence spaces c I (M ), c I 0 (M ), m I (M ) and m I 0 (M ) us... more In this article we introduce the sequence spaces c I (M ), c I 0 (M ), m I (M ) and m I 0 (M ) using the Orlicz function M . We study some of the properties like solid, symmetric, sequence algebra, etc and prove some inclusion relations.
and Technology (VAST) and Springer Science +Business Media Singapore. This e-offprint is for pers... more and Technology (VAST) and Springer Science +Business Media Singapore. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
In this paper we introduce certain new sequence spaces of fuzzy numbers defined by Iconvergence u... more In this paper we introduce certain new sequence spaces of fuzzy numbers defined by Iconvergence using sequences of Orlicz functions and a difference operator of order m. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces.
Journal of the Egyptian Mathematical Society, 2016
An ideal I is a family of subsets of N Â N which is closed under taking finite unions and subsets... more An ideal I is a family of subsets of N Â N which is closed under taking finite unions and subsets of its elements. In this article, the concept of lacunary ideal convergence of double sequences has been introduced. Also the relation between lacunary ideal convergent and lacunary Cauchy double sequences has been established. Furthermore, the notions of lacunary ideal limit point and lacunary ideal cluster points have been introduced and find the relation between these two notions. Finally, we have studied the properties such as solidity, monotonic.
This paper presents the following definition, which is a natural combination of the definitions f... more This paper presents the following definition, which is a natural combination of the definitions for asymptotically equivalent, I-statistically limit and I-lacunary statistical convergence. Let θ be a lacunary sequence; the two nonnegative sequences x = (x k ) and y = (y k ) are said to be I-asymptotically lacunary statistical equivalent of multiple L provided that for every > 0, and δ > 0, ∼ y) and simply I-asymptotically lacunary statistical equivalent if L = 1.
In this article we introduce the lacunary difference sequence spaces defined by Musielak–Orlicz f... more In this article we introduce the lacunary difference sequence spaces defined by Musielak–Orlicz functions and study their algebraic and topological properties. Also we obtain some relations related to these spaces.
An ideal I is a family of subsets of positive integers N which is closed under taking finite unio... more An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In this paper, we introduce the concepts of ideal ?-convergence, ideal ?-Cauchy and ideal ?-bounded sequence in locally solid Riesz space endowed with the topology ?. Some basic properties of these concepts has been investigated. We also examine the ideal ?-continuity of a mapping defined on locally solid Riesz space.
Journal of the Egyptian Mathematical Society, 2014
In this article we introduce paranorm ideal convergent sequence spaces using Zweier transform and... more In this article we introduce paranorm ideal convergent sequence spaces using Zweier transform and Orlicz function. We study some topological and algebraic properties. Further we prove some inclusion relations related to these new spaces. MATHEMATICS SUBJECT CLASSIFICATION: 40A05; 40D25; 40G15 ª 2013 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.
We introduce the concept of (λ,μ)-statistical convergence in n-normed spaces, where λ=(λ r ) and ... more We introduce the concept of (λ,μ)-statistical convergence in n-normed spaces, where λ=(λ r ) and μ=(μ s ) are two non-decreasing sequences of positive real numbers, each tending to ∞ and such that λ r+1 ≤λ r +1, λ 1 =1; μ s+1 ≤μ s +1, μ 1 =1. Some inclusion relations between the sets of statistically convergent and (λ,μ)-statistically convergent double sequences are established. We find its relation to statistical convergence, (C,1,1)-summability and strong (V,λ,μ)-summability in n-normed spaces.
In this article we study the noton of I-monotonic sequences. We prove the decomposition theorem a... more In this article we study the noton of I-monotonic sequences. We prove the decomposition theorem and generalize some of the results on monotonic sequences. We also introduce I-convergent series and studied some results.
In this article, we introduce the lacunary generalized difference double paranormed sequence spac... more In this article, we introduce the lacunary generalized difference double paranormed sequence spaces 2
In this article we introduce the sequence spaces ( , M, , p, q, v , ( , M, , p, q, v , and ( , M,... more In this article we introduce the sequence spaces ( , M, , p, q, v , ( , M, , p, q, v , and ( , M, , p, q, v and study their algebraic and topological properties. Also we obtain some inclusion relations. ξ N m Δ 1 ) ξ N m Δ 0 ) ξ N m Δ ∞ )
In this article we introduce the sequence spaces c I (Λ) , c I 0 (Λ) , m I (Λ) and m I 0 (Λ) asso... more In this article we introduce the sequence spaces c I (Λ) , c I 0 (Λ) , m I (Λ) and m I 0 (Λ) associated with the multiplier sequence Λ = (λ k ) of non-zero scalars. We study the different algebraic and topological properties of these sequence spaces like solidness, symmetricity, sequence algebra, convergence free etc. Also we characterize the multiplier problem and obtain some inclusion relation involving these sequence spaces. : 40A05, 40C05.
In this article we introduced the sequence spaces ( ), 0 ( ), ( ) and 0 ( ) for = ( ), a sequence... more In this article we introduced the sequence spaces ( ), 0 ( ), ( ) and 0 ( ) for = ( ), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces. We prove the decomposition theorem and obtain some inclusion relations. c ⃝2009 Mathematical Institute Slovak Academy of Sciences 2000 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 40A05, 46A45. K e y w o r d s: ideal, filter, -convergent, -null, paranorm.
Acta Mathematicae Applicatae Sinica, English Series, 2011
In this article we introduce the sequence spaces c I (M ), c I 0 (M ), m I (M ) and m I 0 (M ) us... more In this article we introduce the sequence spaces c I (M ), c I 0 (M ), m I (M ) and m I 0 (M ) using the Orlicz function M . We study some of the properties like solid, symmetric, sequence algebra, etc and prove some inclusion relations.
and Technology (VAST) and Springer Science +Business Media Singapore. This e-offprint is for pers... more and Technology (VAST) and Springer Science +Business Media Singapore. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
In this paper we introduce certain new sequence spaces of fuzzy numbers defined by Iconvergence u... more In this paper we introduce certain new sequence spaces of fuzzy numbers defined by Iconvergence using sequences of Orlicz functions and a difference operator of order m. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces.
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