Articles with "bigr" as a keyword



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Extensions of interpolation between the arithmetic-geometric mean inequality for matrices

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Published in 2017 at "Journal of Inequalities and Applications"

DOI: 10.1186/s13660-017-1485-x

Abstract: In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if A, B, X are n×n$n\times n$ matrices, then ∥AXB∗∥2≤∥f1(A∗A)Xg1(B∗B)∥∥f2(A∗A)Xg2(B∗B)∥, $$\begin{aligned} \bigl\Vert AXB^{*} \bigr\Vert… read more here.

Keywords: bigr; vert bigl; vert; bigr vert ... See more keywords
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Asymptotics and oscillation of higher-order functional dynamic equations with Laplacian and deviating arguments

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Published in 2017 at "Advances in Difference Equations"

DOI: 10.1186/s13662-016-1065-2

Abstract: In this paper, we deal with the asymptotics and oscillation of the solutions of higher-order nonlinear dynamic equations with Laplacian and mixed nonlinearities of the form {rn−1(t)ϕαn−1[(rn−2(t)(⋯(r1(t)ϕα1[xΔ(t)])Δ⋯)Δ)Δ]}Δ+∑ν=0Npν(t)ϕγν(x(gν(t)))=0 $$\begin{aligned}& \bigl\{ r_{n-1}(t) \phi_{\alpha_{n-1}} \bigl[ \bigl(r_{n-2}(t) \bigl(\cdots \bigl(r_{1}(t)\phi… read more here.

Keywords: bigl; bigr; equations laplacian; higher order ... See more keywords
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Oscillation criteria for third-order functional half-linear dynamic equations

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Published in 2017 at "Advances in Difference Equations"

DOI: 10.1186/s13662-017-1164-8

Abstract: In this paper, we study the third-order functional dynamic equation {r2(t)ϕα2([r1(t)ϕα1(xΔ(t))]Δ)}Δ+q(t)ϕα(x(g(t)))=0,$$ \bigl\{ r_{2}(t)\phi_{\alpha_{2}} \bigl( \bigl[ r_{1}(t) \phi _{\alpha _{1}} \bigl( x^{\Delta}(t) \bigr) \bigr] ^{\Delta} \bigr) \bigr\} ^{\Delta}+q(t)\phi_{\alpha} \bigl( x\bigl(g(t)\bigr) \bigr) =0, $$ on an upper-unbounded… read more here.

Keywords: bigl; order functional; bigr; order ... See more keywords
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Oscillation of third order nonlinear damped dynamic equation with mixed arguments on time scales

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Published in 2018 at "Advances in Difference Equations"

DOI: 10.1186/s13662-018-1654-3

Abstract: AbstractThe objective of this paper is to offer sufficient conditions for the oscillation of all solutions of the third order nonlinear damped dynamic equation with mixed arguments of the form (r2(r1(yΔ)α)Δ)Δ(t)+p(t)ψ(t,yΔ(a(t)))+q(t)f(t,y(g(t)))=0$$\bigl(r_{2}\bigl(r_{1}\bigl(y^{\Delta}\bigr)^{\alpha}\bigr)^{\Delta}\bigr)^{\Delta}(t)+p(t)\psi \bigl(t,y^{\Delta}\bigl(a(t)\bigr)\bigr)+q(t)f\bigl(t,y\bigl(g(t)\bigr) \bigr)=0 $$ on… read more here.

Keywords: bigl; nonlinear damped; bigr; third order ... See more keywords
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Oscillation for second-order half-linear delay damped dynamic equations on time scales

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Published in 2019 at "Advances in Difference Equations"

DOI: 10.1186/s13662-019-2136-y

Abstract: AbstractWe investigate oscillation of second-order half-linear variable delay damped dynamic equations [a(t)|xΔ(t)|λ−1xΔ(t)]Δ+b(t)|xΔ(t)|λ−1xΔ(t)+p(t)|x(δ(t))|λ−1x(δ(t))=0$$ \bigl[a(t) \bigl\vert x^{\Delta }(t) \bigr\vert ^{\lambda -1}x^{\Delta }(t) \bigr]^{\Delta }+b(t) \bigl\vert x ^{\Delta }(t) \bigr\vert ^{\lambda -1}x^{\Delta }(t)+p(t) \bigl\vert x \bigl(\delta (t) \bigr)… read more here.

Keywords: bigl; bigr; delta; vert ... See more keywords
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Oscillation theorems for three classes of conformable fractional differential equations

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Published in 2019 at "Advances in Difference Equations"

DOI: 10.1186/s13662-019-2247-5

Abstract: AbstractIn this paper, we consider the oscillation theory for fractional differential equations. We obtain oscillation criteria for three classes of fractional differential equations of the forms Tαt0x(t)+∑i=1mpi(t)x(τi(t))=0,t⩾t0,Tαt0(r(t)(Tαt0(x(t)+p(t)x(τ(t))))β)+q(t)xβ(σ(t))=0,t⩾t0, $$\begin{aligned}& T_{\alpha}^{t_{0}} x(t)+\sum_{i=1}^{m}p_{i}(t)x \bigl(\tau_{i}(t)\bigr)=0,\quad t\geqslant t_{0}, \\& T_{\alpha}^{t_{0}}… read more here.

Keywords: bigl; bigr; oscillation; fractional differential ... See more keywords