Sufficient Condition for Convergence of Lagrange–Sturm–Liouville Processes in Terms of One-Sided Modulus of Continuity

2018 ◽  
Vol 58 (11) ◽  
pp. 1716-1727
Author(s):  
A. Yu. Trynin
Keyword(s):  
Modulus Of Continuity ◽  
Sufficient Condition ◽  
Sturm Liouville

Modulus of continuity and convergence of subsequences of Vilenkin–Fejér means in martingale Hardy spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giorgi Tutberidze
Keyword(s):  
Hardy Space ◽  
Modulus Of Continuity ◽  
Hardy Spaces ◽  
Lebesgue Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Fejér Means ◽  
Necessary And Sufficient

Abstract In this paper, we find a necessary and sufficient condition for the modulus of continuity for which subsequences of Fejér means with respect to Vilenkin systems are bounded from the Hardy space H p {H_{p}} to the Lebesgue space L p {L_{p}} for all 0 < p < 1 2 {0<p<\frac{1}{2}} .

scholarly journals On controllability for a class of second-order differential inclusions

2011 ◽  
Vol 27 (1) ◽  
pp. 34-40
Author(s):  
AURELIAN CERNEA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusion ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Second Order ◽  
Sufficient Condition ◽  
Liouville Type ◽  
Sturm Liouville ◽  
The Right

By using a suitable fixed point theorem a sufficient condition for controllability is obtained for a Sturm-Liouville type differential inclusion in the case when the right hand side has convex values.

Sturm–Liouville problems with indefinite weights and Everitt's inequality

1996 ◽  
Vol 126 (5) ◽  
pp. 1097-1112 ◽  
Author(s):  
Hans Volkmer
Keyword(s):  
Spectral Properties ◽  
Eigenvalue Problems ◽  
Baire Category ◽  
Integral Inequalities ◽  
Sufficient Condition ◽  
Indefinite Weights ◽  
Sturm Liouville ◽  
Indefinite Problems

It is shown that spectral properties of Sturm–Liouville eigenvalue problems with indefinite weights are related to integral inequalities studied by Everitt. A result of Beals on indefinite problems leads to a sufficient condition for the validity of such an inequality. A Baire category argument is used to show that, in general, the inequality under consideration does not hold.

scholarly journals On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Józef Banaś ◽  
Rafał Nalepa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Modulus Of Continuity ◽  
Existence Result ◽  
Sufficient Condition ◽  
Hölder Condition ◽  
Fredholm Type ◽  
Relative Compactness ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

We are going to study the space of real functions defined on a bounded metric space and having growths tempered by a modulus of continuity. We prove also a sufficient condition for the relative compactness in the mentioned function space. Using that condition and the classical Schauder fixed point theorem, we show the existence theorem for some quadratic integral equations of Fredholm type in the space of functions satisfying the Hölder condition. An example illustrating the mentioned existence result is also included.

scholarly journals Positive Solutions for Sturm-Liouville Boundary Value Problems in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Su ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Condition ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
The Fixed Point Theorem

We consider the existence of single and multiple positive solutions for a second-order Sturm-Liouville boundary value problem in a Banach space. The sufficient condition for the existence of positive solution is obtained by the fixed point theorem of strict set contraction operators in the frame of the ODE technique. Our results significantly extend and improve many known results including singular and nonsingular cases.

scholarly journals Existence and uniqueness of mild solutions for a fractional differential equation under Sturm-Liouville boundary conditions when the data function is of Lipschitzian type

2020 ◽  
Vol 53 (1) ◽  
pp. 167-173
Author(s):  
Jackie Harjani ◽  
Belen López ◽  
Kishin Sadarangani
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Type Inequality ◽  
Sufficient Condition ◽  
Fractional Boundary Value Problem ◽  
Data Function ◽  
Sturm Liouville ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

AbstractIn this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of Lipschitzian type. Moreover, we present an application of our result to the eigenvalues problem and its connection with a Lyapunov-type inequality.

The Current Situation in Chemical Stabilization of Biological Materials

1972 ◽  
Vol 30 ◽  
pp. 132-133
Author(s):  
John H. Luft
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Osmium Tetroxide ◽  
Molecular Level ◽  
Cross Linking ◽  
Chemical Stabilization ◽  
Specimen Preparation ◽  
Sufficient Condition ◽  
Radio Telescopes

With information processing devices such as radio telescopes, microscopes or hi-fi systems, the quality of the output often is limited by distortion or noise introduced at the input stage of the device. This analogy can be extended usefully to specimen preparation for the electron microscope; fixation, which initiates the processing sequence, is the single most important step and, unfortunately, is the least well understood. Although there is an abundance of fixation mixtures recommended in the light microscopy literature, osmium tetroxide and glutaraldehyde are favored for electron microscopy. These fixatives react vigorously with proteins at the molecular level. There is clear evidence for the cross-linking of proteins both by osmium tetroxide and glutaraldehyde and cross-linking may be a necessary if not sufficient condition to define fixatives as a class.

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