Compact Operators on the Sets of Fractional Difference Sequences

Özger, Faruk

doi:10.16984/saufenbilder.463368

Cited by 4 publications

(3 citation statements)

References 38 publications

(37 reference statements)

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“…While the Hausdor¤ measure of non-compactness is established to study modulus of noncompact convexity which is important in the geometry of Banach and Hilbert spaces it is also used to …nd necessary and su¢ cient conditions for a matrix operator on a given sequence space to be a compact operator (see [24,25,32]). Topological properties of certain sets of sequence spaces are investigated in the papers [1-3, 7-10, 13, 16, 21-23, 31, 33, 34] and [40].…”

Section: Resultsmentioning

confidence: 99%

Some Geometric Characterizations of a Fractional Banach Set

Özger¹

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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This paper is devoted to investigate the modular structure of a fractional Banach set of sequences and prove that this set is re ‡exive and convex and it possesses uniform Opial, (), (L) and (H) properties. The convexity of the set is investigated by the notion of extreme points. These properties play an important role both in the study of …xed point theory and in the geometric characterizations of the Banach sets of sequences. This study extends the scope of the fractional calculus and it is related with …xed point and approximation theories.

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Section: Resultsmentioning

confidence: 99%

Some Geometric Characterizations of a Fractional Banach Set

Özger¹

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…Many authors have made efforts to apply Hausdorff measure of noncompactness to find compactness conditions of certain sets of sequences during the past decade [24][25][26][27]. Note that, necessary and sufficient compactness conditions for a matrix operator from fractional sets of sequences c 0 (∆ (α) ), c(∆ (α) ) and ℓ∞(∆ (α) ) to the classical sets of sequences have been very recently determined in [28].…”

Section: Introductionmentioning

confidence: 99%

Characterizations of compact operators on ℓ_p−type fractional sets of sequences

Özger

2019

Demonstratio Mathematica

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Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp−type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.

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“…We refer to to establish the necessary and sufficient conditions for a matrix operator to be a compact operator in the classes (X, Y ) , where X = ℓ p (∆ ( α) ) (1 ≤ p < ∞) and Y is any of the spaces c 0 , c , and ℓ 1 . The necessary and sufficient compactness conditions for a matrix operator from fractional sets of sequences c 0 (∆ (α) ) , c(∆ ( α) ) , and ℓ ∞ (∆ ( α) ) to the classical sets of sequences have been very recently determined in [25]. Fractional Banach set of difference sequences ℓ(∆ ( α) , p) was geometrically characterized and its modular structure was investigated in [24].…”

Section: Introductionmentioning

confidence: 99%

Some general results on fractional Banach sets

Özger¹

2019

Turk J Math

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The gamma function which is expressed by an improper integral is used to establish the fractional difference operators and fractional Banach sets. In this study, we achieve some comprehensive and complementary results related to characterizations of the matrix classes of fractional Banach sets. We also obtain some identities or inequalities for the Hausdorff measure of noncompactness of the corresponding matrix operators, and finally find the necessary and sufficient conditions for those matrix operators to be compact.

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Compact Operators on the Sets of Fractional Difference Sequences

Cited by 4 publications

References 38 publications

Some Geometric Characterizations of a Fractional Banach Set

Some Geometric Characterizations of a Fractional Banach Set

Characterizations of compact operators on ℓ_p−type fractional sets of sequences

Some general results on fractional Banach sets

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Compact Operators on the Sets of Fractional Difference Sequences

Cited by 4 publications

References 38 publications

Some Geometric Characterizations of a Fractional Banach Set

Some Geometric Characterizations of a Fractional Banach Set

Characterizations of compact operators on ℓp−type fractional sets of sequences

Some general results on fractional Banach sets

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Characterizations of compact operators on ℓ_p−type fractional sets of sequences