On The Paranormed Spaces of Regularly Convergent Double Sequences
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DOI: 10.1007/s00025-017-0693-5
Abstract: In Hardy (Proc Camb Philos 19:86–95, 1916), Hardy defined the normed spaces $$\mathcal {C}_{r}$$Cr and $$\mathcal {C}_{r0}$$Cr0 of all regularly convergent and regularly null double sequences and made convergence factor calculations (i.e. some beta-dual calculations).… read more here.
Keywords: regularly convergent; paranormed spaces; double sequences; spaces regularly ... See more keywords
Fractional difference double sequences of fuzzy numbers
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DOI: 10.1007/s13370-021-00912-7
Abstract: We present double sequence spaces of fuzzy numbers defined using fractional difference operator and Musielak–Orlicz function. Some topological properties for these spaces are presented and some inclusion relations are established. Finally, we formulate and prove… read more here.
Keywords: sequences fuzzy; fuzzy numbers; double sequences; fractional difference ... See more keywords
On the Paranormed Space of Bounded Variation Double Sequences
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DOI: 10.1007/s40840-019-00829-2
Abstract: In this study, as the domain of four-dimensional backward difference matrix in the space $$\mathcal {L}_u(t)$$ L u ( t ) , we introduce the complete paranormed space $$\mathcal {BV}(t)$$ BV ( t ) of… read more here.
Keywords: mathcal mathcal; space; double sequences; paranormed space ... See more keywords
On $\mathcal{I}_{{\theta}_{2}}$-convergence in fuzzy normed spaces
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DOI: 10.1186/s13660-020-02387-9
Abstract: In this study, first, lacunary convergence of double sequences is introduced in fuzzy normed spaces, and basic definitions and theorems about lacunary convergence for double sequences are given in fuzzy normed spaces. Then, we introduce… read more here.
Keywords: lacunary convergence; fuzzy normed; normed spaces; double sequences ... See more keywords
On regularly generated double sequences
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DOI: 10.2298/fil1703809t
Abstract: In this paper, we introduce regularly generated sequences for double sequence of real numbers, and obtain some Tauberian theorems for $(C,1,1)$ summability method using the concept of regularly generated sequence. read more here.
Keywords: regularly generated; generated double; double sequences;
Exponent of convergence for double sequences and selection principles
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DOI: 10.2298/fil1709821d
Abstract: In this paper, we will define the exponent of convergence for double sequences and in that terminology, we will prove tree new theorems in theory of selection principles for double sequences. read more here.
Keywords: exponent convergence; convergence double; selection principles; double sequences ... See more keywords