Benharrat Belaïdi

Complex oscillation of differential polynomials in the unit disc

We consider the complex differential equations f″ + A1(z)f′ + A0(z)f = F and where A0 ≢ 0, A1 and F are analytic functions in the unit disc Δ = {z: |z| < 1}. We obtain results on the order and the exponent of convergence of zero-points in Δ of the differential polynomials gf = d2f″ + d1f′ + d0f with non-simultaneously vanishing analytic coefficients d2, d1, d0. We answer a question posed by J. Tu and C. F. Yi in 2008 for the case of the second order linear differential equations in the unit disc.

Some Properties of Solutions of Second-Order Linear Differential Equations

We study the growth and oscillation of , where and are entire functions of finite order not all vanishing identically and and are two linearly independent solutions of the linear differential equation .

New Inequalities for Convex Sequences with Applications

In this paper, we will show some new inequalities for convex sequences, and we will also make a connection between them and Chebyshev’s inequality, which implies the existence of new class of sequences satisfying Chebyshev’s inequality. We give also some applications and generalization of Haber and Mercer’s inequalities.

On Picard value problem of some difference polynomials

In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order.

On the Growth of Solutions of Some Second Order Linear Differential Equations with Entire Coefficients

Abstract In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation where n≥2 is an integer, Aj (z) (≢0) (j = 1,2) are entire functions with max {σ A(j) : (j = 1,2} < 1, Q (z) = qmzm + ... + q1z + q0 is a nonoonstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove that every solution f (z) ≢ 0 of the above equation is of infinite order and hyper-order 1.

Nonhomogeneous linear differential polynomials generated by solutions of complex differential equations in the unit disc

We consider the complex oscillation of nonhomogeneous linear differential polynomials gk = ∑k j=0 djf +b, where dj (j=0, 1, . . . , k) and b are meromorphic functions of finite [p,q]-order in the unit disc ∆, generated by meromorphic solutions of linear differential equations with meromorphic coefficients of finite [p,q]-order in ∆.

Growth of Meromorphic Solutions of Finite Logarithmic Order of Linear Difference Equations

Abstract In this paper, we deal with the growth and the oscillation of solutions of the linear difference equation an (z) f (z + n) + an-1 (z) f (z + n - 1) + ··· + a1 (z) f (z + 1) + a0 (z) f (z) = 0; where an(z),···, a0(z) are meromorphic functions of finite logarithmic order such that an(z)a0(z) 6≢ 0.

Growth of Logarithmic Derivatives and Their Applications in Complex Differential Equations

We continue the study of the behavior of the growth of logarithmic derivatives. In fact, we prove some relations between the value distribution of solutions of linear differential equations and growth of their logarithmic derivatives. We also give an estimate of the growth of the quotient of two differential polynomials generated by solutions of the equation where and are entire functions.

On the Iterated Exponent of Convergence of Solutions of Linear Differential Equations with Entire and Meromorphic Coefficients

We investigate the zeros of the difference of the derivative of solutions of the higher-order linear differential equations and small functions, where , are entire or meromorphic functions of finite iterated order.

Further Estimations on the Order of Growth and the Type of Meromorphic Functions in the Unit Disc

Abstract In this paper, we will give sufficient conditions to obtain new estimates about the order of growth and the type of meromorphic functions in the unit disc Δ ={z ∊ ℂ :∣ z ∣ < 1} we give also some examples to explain the sharpness of these estimations.