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Differential Inequalities and Starlikeness
Complex Variables, Theory and Application: An International Journal, 2003We study some differential inequalities in the unit disc which imply starlikeness: for example if ƒ (z) = z + Σ∞ n=2 an (ƒ)zn is analytic in D = {z | |z| < 1} and |z(ƒ′′(z) − 1)| ≤ 1 − α, z∊D for some α ] [0, 1), then ƒ is one-to-one on D and ƒ (D) is a starlike domain with respect to the origin.
Richard Fournier, Petru Mocanu
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Differential inequalities for Liapunov functions
Nonlinear Analysis: Theory, Methods & Applications, 1977This chapter discusses differential inequalities for Liapunov functions. It discusses a system of ordinary differential equations x ' = f ( t , x ) where f: [0, ∞) × R n → R n is continuous and it is supposed that there is a function V : [0, ∞) × R n → [0, ∞) that is continuous, locally Lipschitz in x , and satisfies V' 1 ( t , x ) ≤ 0.
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Systems of differential inequalities and stochastic differential equations. III
Journal of Mathematical Physics, 1975Consider the system of stochastic differential equations x′ (t,ω) =f (t,x (t,ω),ω), x (t0,ω) =x0(ω), where f (t,x (t,ω),ω) is a product measurable n-dimensional random vector function whenever x (t,ω) is a product measurable random function, and it satisfies the desired regularity conditions to ensure the existence of solution process.
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Some Differential Inequalities
2019Projekt Operacyjny Polska Cyfrowa POPC.02.03.01-00-0039 ...
Katafiasz, Aleksandra +1 more
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Hyperbolic Differential Inequalities
Journal of the London Mathematical Society, 1967Edmunds, D. E., Williams, Valerie
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
An Integro-Differential Inequality
1983Let u(x,y) ∈ C(2)[0,a] × [0,b]), u(x,0) = u(0,y) = 0 for all 0 ≤ x ≤ a, 0 ≤ y ≤ b. then $$(1)\,\int_0^a {\int_0^b {|u(x,y)u_{xy} (x,y)|dx\,dy\, \leqslant c} } \int_0^a {\int_0^b {|u_{ux} (x,y)|^2 dx\,dy} } $$ (1) where $$C = \frac{{ab}}{{2\sqrt 2 }}.$$ .
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