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Papers by Zinelaâbidine LATREUCH
International Journal of Analysis and Applications, 2015
In this paper, we study the q-analogue of Klamkin-McLenaghan's and Grueb-Reinboldt's ineq... more In this paper, we study the q-analogue of Klamkin-McLenaghan's and Grueb-Reinboldt's inequalities then we use the Riemann-Liouville fractional q-integral to get some new integral results.
The aim of this work is to establish the q-analogue of Hermite-Hadamard inequalities for convex f... more The aim of this work is to establish the q-analogue of Hermite-Hadamard inequalities for convex functions and r-convex functions.
In this paper, we consider uniqueness problems on entire functions that share a small periodic en... more In this paper, we consider uniqueness problems on entire functions that share a small periodic entire functions with their shifts and difference operators, we improve also some results due to B. Chen, Z. X. Chen and S. Li.
Opuscula Mathematica, 2015
In this paper, we continue the study of some properties on the growth and oscillation of solution... more In this paper, we continue the study of some properties on the growth and oscillation of solutions of linear differential equations with entire coefficients of the type
International Journal of Analysis, 2014
We continue the study of the behavior of the growth of logarithmic derivatives. In fact, we prove... more 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 + ( ) + ( ) = 0, where ( ) and ( ) are entire functions.
This paper is devoted to studying the growth and oscillation of solutions and their derivatives o... more This paper is devoted to studying the growth and oscillation of solutions and their derivatives of equations of the type f′′+A(z)f′+B(z)f=F(z)f''+A(z)f'+B(z)f =F(z)f′′+A(z)f′+B(z)f=F(z), where A(z),B(z)neq0A(z),B(z)\neq0A(z),B(z)neq0 and F(z)neq0F(z)\neq 0F(z)neq0 are meromorphic functions of finite order.
We study the uniqueness for entire functions that share small functions of finite order with diff... more We study the uniqueness for entire functions that share small functions of finite order with difference operators applied to the entire functions. In particular, we generalize of a result in [2].
The main purpose of this paper is to study the growth of certain combinations of entire solutions... more The main purpose of this paper is to study the growth of certain combinations of
entire solutions of higher order complex linear differential equations.
In this paper, we deal with the growth and oscillation of w = d1f1 + d2f2, where d1, d2 are merom... more In this paper, we deal with the growth and oscillation of w = d1f1 + d2f2, where d1, d2 are meromorphic functions of finite iterated p−order that are not all vanishing identically and f1, f2 are two linearly independent meromorphic solutions in the unit disc ∆ = {z ∈ C : |z| < 1} satisfying δ (∞, fj) > 0, (j = 1, 2), of the linear differential equation
This paper is devoted to studying the growth and oscillation of higher order differential polynom... more This paper is devoted to studying the growth and oscillation of higher order differential polynomial with meromorphic coefficients generated by meromorphic solutions of the linear differential equation
![Research paper thumbnail of SOME PROPERTIES OF COMBINATION OF SOLUTIONS TO SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH ANALYTIC COEFFICIENTS OF [P;Q]-ORDER IN THE UNIT DISC](https://attachments.academia-assets.com/35823452/thumbnails/1.jpg)
](In this paper, we consider some properties on the growth and oscillation of combination of soluti... more In this paper, we consider some properties on the growth and oscillation of combination of solutions of the linear dierential equation
In this paper, we study the complex oscillation of solutions and their derivatives of the di eren... more In this paper, we study the complex oscillation of solutions and
their derivatives of the di erential equation
f00 + A(z) f0 + B (z) f = F (z) ;
where A(z) ;B (z) (6 0) and F (z) (6 0) are meromorphic functions of nite
iterated p-order in the unit disc = fz : jzj < 1g.
In this paper, we will give sufficient conditions to obtain new estimates about the order of grow... more 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.
In this paper, we continue the study of some properties on the growth and oscillation of solution... more In this paper, we continue the study of some properties on the growth and oscillation of solutions of linear differential equations with entire coefficients.
In this paper, we study the growth and the oscillation of solutions of linear difference equation... more In this paper, we study the growth and the oscillation of solutions of linear difference equations with meromorphic coefficients. Also, we investigate the growth of difference polynomials generated by meromorphic solutions of some difference equations. We improve and generalize some results due to Z. X. Chen, I.
In this paper, we investigate the growth and oscillation of higher order differential polynomial ... more In this paper, we investigate the growth and oscillation of higher order differential polynomial with meromorphic coefficients in the unit disc ∆ = {z : |z| < 1} generated by solutions of the linear differential equation
In this paper we will show some new inequalities for convex functions, and we will also make a co... more In this paper we will show some new inequalities for convex functions, and we will also make a connection between it and Gruss inequality, which implies the existence of new class of functions satis ed Gruss inequality.
In this paper, we give some estimations about the growth of logarithmic derivative of meromorphic... more In this paper, we give some estimations about the growth of logarithmic derivative of meromorphic and entire functions and their applications in the theory of differential equations. We give also some examples to explain the sharpness of our results.
International Journal of Analysis and Applications, 2015
In this paper, we study the q-analogue of Klamkin-McLenaghan's and Grueb-Reinboldt's ineq... more In this paper, we study the q-analogue of Klamkin-McLenaghan's and Grueb-Reinboldt's inequalities then we use the Riemann-Liouville fractional q-integral to get some new integral results.
The aim of this work is to establish the q-analogue of Hermite-Hadamard inequalities for convex f... more The aim of this work is to establish the q-analogue of Hermite-Hadamard inequalities for convex functions and r-convex functions.
In this paper, we consider uniqueness problems on entire functions that share a small periodic en... more In this paper, we consider uniqueness problems on entire functions that share a small periodic entire functions with their shifts and difference operators, we improve also some results due to B. Chen, Z. X. Chen and S. Li.
Opuscula Mathematica, 2015
In this paper, we continue the study of some properties on the growth and oscillation of solution... more In this paper, we continue the study of some properties on the growth and oscillation of solutions of linear differential equations with entire coefficients of the type
International Journal of Analysis, 2014
We continue the study of the behavior of the growth of logarithmic derivatives. In fact, we prove... more 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 + ( ) + ( ) = 0, where ( ) and ( ) are entire functions.
This paper is devoted to studying the growth and oscillation of solutions and their derivatives o... more This paper is devoted to studying the growth and oscillation of solutions and their derivatives of equations of the type f′′+A(z)f′+B(z)f=F(z)f''+A(z)f'+B(z)f =F(z)f′′+A(z)f′+B(z)f=F(z), where A(z),B(z)neq0A(z),B(z)\neq0A(z),B(z)neq0 and F(z)neq0F(z)\neq 0F(z)neq0 are meromorphic functions of finite order.
We study the uniqueness for entire functions that share small functions of finite order with diff... more We study the uniqueness for entire functions that share small functions of finite order with difference operators applied to the entire functions. In particular, we generalize of a result in [2].
The main purpose of this paper is to study the growth of certain combinations of entire solutions... more The main purpose of this paper is to study the growth of certain combinations of
entire solutions of higher order complex linear differential equations.
In this paper, we deal with the growth and oscillation of w = d1f1 + d2f2, where d1, d2 are merom... more In this paper, we deal with the growth and oscillation of w = d1f1 + d2f2, where d1, d2 are meromorphic functions of finite iterated p−order that are not all vanishing identically and f1, f2 are two linearly independent meromorphic solutions in the unit disc ∆ = {z ∈ C : |z| < 1} satisfying δ (∞, fj) > 0, (j = 1, 2), of the linear differential equation
This paper is devoted to studying the growth and oscillation of higher order differential polynom... more This paper is devoted to studying the growth and oscillation of higher order differential polynomial with meromorphic coefficients generated by meromorphic solutions of the linear differential equation
In this paper, we consider some properties on the growth and oscillation of combination of soluti... more In this paper, we consider some properties on the growth and oscillation of combination of solutions of the linear dierential equation
In this paper, we study the complex oscillation of solutions and their derivatives of the di eren... more In this paper, we study the complex oscillation of solutions and
their derivatives of the di erential equation
f00 + A(z) f0 + B (z) f = F (z) ;
where A(z) ;B (z) (6 0) and F (z) (6 0) are meromorphic functions of nite
iterated p-order in the unit disc = fz : jzj < 1g.
In this paper, we will give sufficient conditions to obtain new estimates about the order of grow... more 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.
In this paper, we continue the study of some properties on the growth and oscillation of solution... more In this paper, we continue the study of some properties on the growth and oscillation of solutions of linear differential equations with entire coefficients.
In this paper, we study the growth and the oscillation of solutions of linear difference equation... more In this paper, we study the growth and the oscillation of solutions of linear difference equations with meromorphic coefficients. Also, we investigate the growth of difference polynomials generated by meromorphic solutions of some difference equations. We improve and generalize some results due to Z. X. Chen, I.
In this paper, we investigate the growth and oscillation of higher order differential polynomial ... more In this paper, we investigate the growth and oscillation of higher order differential polynomial with meromorphic coefficients in the unit disc ∆ = {z : |z| < 1} generated by solutions of the linear differential equation
In this paper we will show some new inequalities for convex functions, and we will also make a co... more In this paper we will show some new inequalities for convex functions, and we will also make a connection between it and Gruss inequality, which implies the existence of new class of functions satis ed Gruss inequality.
In this paper, we give some estimations about the growth of logarithmic derivative of meromorphic... more In this paper, we give some estimations about the growth of logarithmic derivative of meromorphic and entire functions and their applications in the theory of differential equations. We give also some examples to explain the sharpness of our results.