scholarly journals Some Remarks on Borel Type Ideals

2009 ◽  
Vol 37 (2) ◽  
pp. 724-727 ◽  
Author(s):  
Mircea Cimpoeaş
Keyword(s):  
Borel Type

scholarly journals Fuzzy Differential Subordinations Based Upon the Mittag-Leffler Type Borel Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1023
Author(s):  
Hari Mohan Srivastava ◽  
Sheza M. El-Deeb
Keyword(s):  
Fuzzy Systems ◽  
Special Functions ◽  
Univalent Functions ◽  
Local Symmetry ◽  
Open Unit ◽  
Fuzzy Membership Functions ◽  
Non Local ◽  
Differential Subordinations ◽  
Two Parameter ◽  
Borel Type

In this paper, we investigate several fuzzy differential subordinations that are connected with the Borel distribution series Bλ,α,β(z) of the Mittag-Leffler type, which involves the two-parameter Mittag-Leffler function Eα,β(z). Using the above-mentioned operator Bλ,α,β, we also introduce and study a class Mλ,α,βFη of holomorphic and univalent functions in the open unit disk Δ. The Mittag-Leffler-type functions, which we have used in the present investigation, belong to the significantly wider family of the Fox-Wright function pΨq(z), whose p numerator parameters and q denominator parameters possess a kind of symmetry behavior in the sense that it remains invariant (or unchanged) when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. Here, in this article, we have used such special functions in our study of a general Borel-type probability distribution, which may be symmetric or asymmetric. As symmetry is generally present in most works involving fuzzy sets and fuzzy systems, our usages here of fuzzy subordinations and fuzzy membership functions potentially possess local or non-local symmetry features.

scholarly journals On Borel-type methods

1966 ◽  
Vol 18 (3) ◽  
pp. 283-298 ◽  
Author(s):  
David Borwein ◽  
Bruce Lockhart Robertson Shawyer
Keyword(s):  
Borel Type

A Tauberian Theorem for Borel-Type Methods of Summability

1969 ◽  
Vol 21 ◽  
pp. 740-747 ◽  
Author(s):  
D. Borwein
Keyword(s):  
Tauberian Theorem ◽  
Convergent Series ◽  
Summability Method ◽  
Negative Integer ◽  
Exponential Method ◽  
Image Position ◽  
Borel Type ◽  
Cesàro Method

Suppose throughout that α >0, β is real, and Nis a non-negative integer such that αN+ β> 0. A series of complex terms is said to be summable (B, α,β) to l if, as x→ ∞,where sn= a0 + a1 + … + an.The Borel-type summability method (B, α, β) is regular, i.e., all convergent series are summable (B, α,β) to their natural sums; and (B,1, 1) is the standard Borel exponential method B.Our aim in this paper is to prove the following Tauberian theorem.THEOREM. Iƒ(i) p ≧ – ½, an = o(np), and(ii) is summable (B, α,β) to l, then the series is summable by the Cesaro method(C, 2p + 1) to l.

scholarly journals Correction: ``On Borel-type methods''

1967 ◽  
Vol 19 (2) ◽  
pp. 244-244
Author(s):  
David Borwein ◽  
Bruce L. R. Shawyer
Keyword(s):  
Borel Type

scholarly journals Certain Bounds of Regularity of Elimination Ideals on Operations of Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Zongming Lv ◽  
Muhammad Junaid Ali Junjua ◽  
Muhammad Tajammal Tahir ◽  
Khurram Shabbir
Keyword(s):  
Upper Bound ◽  
Degree Sequence ◽  
Borel Type

Elimination ideals are regarded as a special type of Borel type ideals, obtained from degree sequence of a graph, introduced by Anwar and Khalid. In this paper, we compute graphical degree stabilities of K n ∨ C m and K n ∗ C m by using the DVE method. We further compute sharp upper bound for Castelnuovo–Mumford regularity of elimination ideals associated to these families of graphs.

scholarly journals Cesàro and Borel-type summability

1988 ◽  
Vol 103 (4) ◽  
pp. 1108-1108
Author(s):  
David Borwein ◽  
Tom Markovich
Keyword(s):  
Borel Type
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