scholarly journals Estimates ofLpModulus of Continuity of Generalized Bounded Variation Classes

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Heping Wang ◽  
Zhaoyang Wu
Keyword(s):  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Fourier Coefficients ◽  
Necessary Conditions ◽  
Sharp Estimates ◽  
Sufficient And Necessary Conditions ◽  
Special Case

Some sharp estimates of theLp1≤p<∞modulus of continuity of classes ofΛφ-bounded variation are obtained. As direct applications, we obtain estimates of order of Fourier coefficients of functions ofΛφ-bounded variation, and we also characterize some sufficient and necessary conditions for the embedding relationsHpω⊂ΛφBV. Our results include the corresponding known results of the classΛBVas a special case.

scholarly journals Fourier series with small gaps

1989 ◽  
Vol 46 (2) ◽  
pp. 212-219
Author(s):  
P. Isaza ◽  
D. Waterman
Keyword(s):  
Fourier Series ◽  
Trigonometric Series ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Order Condition ◽  
Circle Group ◽  
The Difference ◽  
Bounded Below

AbstractA trigonometric series has “small gaps” if the difference of the orders of successive terms is bounded below by a number exceeding one. Wiener, Ingham and others have shown that if a function represented by such a series exhibits a certain behavior on a large enough subinterval I, this will have consequences for the behavior of the function on the whole circle group. Here we show that the assumption that f is in any one of various classes of functions of generalized bounded variation on I implies that the appropriate order condition holds for the magnitude of the Fourier coefficients. A generalized bounded variation condition coupled with a Zygmundtype condition on the modulus of continuity of the restriction of the function to I implies absolute convergence of the Fourier series.

scholarly journals Bounded sets in the range of anX∗∗-valued measure with bounded variation

2000 ◽  
Vol 23 (1) ◽  
pp. 21-30 ◽  
Author(s):  
B. Marchena ◽  
C. Piñeiro
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Bounded Variation ◽  
Necessary Conditions ◽  
Bounded Set ◽  
Sufficient And Necessary Conditions ◽  
Bounded Sets

LetXbe a Banach space andA⊂Xan absolutely convex, closed, and bounded set. We give some sufficient and necessary conditions in order thatAlies in the range of a measure valued in the bidual spaceX∗∗and having bounded variation. Among other results, we prove thatX∗is a G. T.-space if and only ifAlies inside the range of someX∗∗-valued measure with bounded variation wheneverXAis isomorphic to a Hilbert space.

scholarly journals Weighted multilinear Hardy operators and commutators

2015 ◽  
Vol 27 (5) ◽  
Author(s):  
Zun Wei Fu ◽  
Shu Li Gong ◽  
Shan Zhen Lu ◽  
Wen Yuan
Keyword(s):  
Necessary Conditions ◽  
Morrey Spaces ◽  
Bmo Space ◽  
Weight Functions ◽  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Sharp Estimates ◽  
Sufficient And Necessary Conditions ◽  
Hardy Operators

AbstractIn this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight functions so that the commutators of the weighted multilinear Hardy operators (with symbols in central BMO space) are bounded on the product of central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Riemann–Liouville and Weyl.

A DYNAMICAL MODEL FOR THE PROCESS OF SHARING

2018 ◽  
Vol 21 (06n07) ◽  
pp. 1850016 ◽  
Author(s):  
ULRICH KRAUSE
Keyword(s):  
Multiagent Systems ◽  
Necessary Conditions ◽  
Opinion Dynamics ◽  
Ring Structure ◽  
Dynamical Model ◽  
Equal Distribution ◽  
Sufficient And Necessary Conditions ◽  
Special Case

The paper introduces a general sharing structure and presents sufficient and necessary conditions for the agents to approach by the dynamics of sharing an equal distribution of assets. For the special case of a ring structure with a uniform sharing rate, robustness is analyzed in case the rate does change during the process of sharing. The search for an equal distribution is similar to that for consensus in opinion dynamics and multiagent systems as a result of which tools from the latter are used in proving the results.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

Perfect colorings of patterns with multiple orbits

2019 ◽  
Vol 75 (6) ◽  
pp. 814-826
Author(s):  
Allan Junio ◽  
Ma. Lailani Walo
Keyword(s):  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

This paper studies colorings of patterns with multiple orbits, particularly those colorings where the orbits share colors. The main problem is determining when such colorings become perfect. This problem is attacked by characterizing all perfect colorings of patterns through the construction of sufficient and necessary conditions for a coloring to be perfect. These results are then applied on symmetrical objects to construct both perfect and non-perfect colorings.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

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