An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

2016 ◽  
Vol 94 (3) ◽  
pp. 618-631 ◽  
Author(s):  
Constantin Buşe ◽  
Donal O’Regan ◽  
Olivia Saierli
2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Constantin Buse ◽  
Aftab Khan ◽  
Gul Rahmat ◽  
Afshan Tabassum

2020 ◽  
Vol 26 (2) ◽  
pp. 185-192
Author(s):  
Sunanda Naik ◽  
Pankaj K. Nath

AbstractIn this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular, we obtain a well-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 2009, 2, 304–311]. Also we consider the adjoint {\mathcal{A}^{b,c}} for {b>0} of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces {B_{\alpha+(c-1)}^{p,q}} for {c>1}.


2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Michael Herrmann ◽  
Karsten Matthies

AbstractWe study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein–Rutman arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.


Author(s):  
Maxime Martineau ◽  
Romain Raveaux ◽  
Donatello Conte ◽  
Gilles Venturini

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Saqib Hussain ◽  
Akhter Rasheed ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus

We investigate some subclasses ofk-uniformly convex andk-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.


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