On Existence and a Dominated Convergence Theorem for Weighted g-Summability

1972 ◽  
Vol 34 (2) ◽  
pp. 479
Author(s):  
Fred M. Wright ◽  
Melvin L. Klasi
Keyword(s):  
Convergence Theorem ◽  
Dominated Convergence

scholarly journals A dominated convergence theorem for Eisenstein series

2021 ◽  
Author(s):  
Johann Franke
Keyword(s):  
Fourier Series ◽  
Dirichlet Series ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Convergence Theorem ◽  
Rational Functions ◽  
New Approach ◽  
Series Representations ◽  
Dominated Convergence ◽  
Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

scholarly journals On Fuzzy Henstock-Kurzweil-Stieltjes-♦-Double Integral on Time scales

2021 ◽  
Vol 2 (2) ◽  
pp. 38-49
Author(s):  
David AFARIOGUN ◽  
Adesanmi MOGBADEMU ◽  
Hallowed OLAOLUWA
Keyword(s):  
Uniform Convergence ◽  
Time Scales ◽  
Convergence Theorem ◽  
Monotone Convergence ◽  
Double Integral ◽  
Monotone Convergence Theorem ◽  
Integrable Functions ◽  
Dominated Convergence

We introduce and study some properties of fuzzy Henstock-Kurzweil-Stietljes-$ \Diamond $-double integral on time scales. Also, we state and prove the uniform convergence theorem, monotone convergence theorem and dominated convergence theorem for the fuzzy Henstock-Kurzweil Stieltjes-$\Diamond$-double integrable functions on time scales.

scholarly journals A DOMINATED CONVERGENCE THEOREM IN THE K-H INTEGRAL

2003 ◽  
Vol 7 (3) ◽  
pp. 507-512
Author(s):  
Jitan Lu ◽  
Peng-Yee Lee
Keyword(s):  
Convergence Theorem ◽  
Dominated Convergence

scholarly journals Fatou's Lemma and Lebesgue's convergence theorem for measures

2000 ◽  
Vol 13 (2) ◽  
pp. 137-146 ◽  
Author(s):  
Onésimo Hernández-Lerma ◽  
Jean B. Lasserre
Keyword(s):  
Asymptotic Behavior ◽  
Banach Spaces ◽  
General Result ◽  
Convergence Theorem ◽  
Convergence Theorems ◽  
Vector Lattices ◽  
Fatou’S Lemma ◽  
Dominated Convergence ◽  
Special Case ◽  
Fatou's Lemma

Analogues of Fatou's Lemma and Lebesgue's convergence theorems are established for ∫fdμn when {μn} is a sequence of measures. A “generalized” Dominated Convergence Theorem is also proved for the asymptotic behavior of ∫fndμn and the latter is shown to be a special case of a more general result established in vector lattices and related to the Dunford-Pettis property in Banach spaces.

scholarly journals Employing Kuratowski measure of non-compactness for positive solutions of system of singular fractional q-differential equations with numerical effects

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2971-2989
Author(s):  
Mohammad Samei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Convergence Theorem ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Liouville Type ◽  
Integral Boundary ◽  
Dominated Convergence

In this work, we investigate the existence of solutions for the system of two singular fractional q-differential equations under integral boundary conditions via the concept of Caputo fractional q-derivative and fractional Riemann-Liouville type q-integral. Some new existence results are obtained by applying Krattowski measure of non-compactness. Also, the Darbo?s fixed point theorem and the Lebesgue dominated convergence theorem are the main tools in deriving our proofs. Lastly, we present an example illustrating the primary effects.

The a-Local Operator Problem

1959 ◽  
Vol 11 ◽  
pp. 583-592 ◽  
Author(s):  
Louis de Branges
Keyword(s):  
Fourier Transform ◽  
Total Variation ◽  
Convergence Theorem ◽  
Borel Measure ◽  
Local Operator ◽  
Operator Problem ◽  
Dominated Convergence ◽  
The Fourier Transform ◽  
Image Position ◽  
The Right

Let be the Fourier transform of a Borel measure of finite total variation. The formulacan be justified if the integral on the right converges absolutely. ForwhereNow let h → 0 in both sides of this equation and use the Lebesgue dominated convergence theorem.

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