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Papers by Dr. Samir Al Mohammady

Research paper thumbnail of Global behavior of a third-order rational difference equation

The journal of mathematics and computer science, Jul 3, 2021

In this paper, we investigate the behavior of solutions of the difference equation x n+1 = α (x n... more In this paper, we investigate the behavior of solutions of the difference equation x n+1 = α (x n−1 + x n−2) + (α − 1) x n−1 x n−2 x n−1 x n−2 + α , n = 0, 1, 2,. .. , where the initial conditions x −2 , x −1 , x 0 are arbitrary non-negative real numbers and the parameter α ∈ [1, ∞). More precisely, we study the boundedness, stability, and oscillation of the solutions of this equation.

Research paper thumbnail of On (N,M)-a-normal And (N, M)-a-quasinormal Semi- Hilbert Space Operators

arXiv (Cornell University), Dec 4, 2019

The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian sp... more The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product h | k A := Ah | k h, k ∈ H induces a semi-norm. A. This makes H into a semi-Hilbertian space. An operator T ∈ B A

Research paper thumbnail of On <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span>-$A$-normal and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span>-$A$-quasinormal semi-Hilbertian space operators

Mathematica Bohemica

We obtain some new sufficient conditions for the oscillation of the solutions of the second-order... more We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known ones.

Research paper thumbnail of Global behavior of a third-order rational difference equation

Journal of Mathematics and Computer Science, 2021

In this paper, we investigate the behavior of solutions of the difference equation x n+1 = α (x n... more In this paper, we investigate the behavior of solutions of the difference equation x n+1 = α (x n−1 + x n−2) + (α − 1) x n−1 x n−2 x n−1 x n−2 + α , n = 0, 1, 2,. .. , where the initial conditions x −2 , x −1 , x 0 are arbitrary non-negative real numbers and the parameter α ∈ [1, ∞). More precisely, we study the boundedness, stability, and oscillation of the solutions of this equation.

Research paper thumbnail of Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenth-order

Journal of Mathematics and Computer Science, 2021

The main goal of this paper, is to obtain the forms of the solutions of the following nonlinear f... more The main goal of this paper, is to obtain the forms of the solutions of the following nonlinear fifteenth-order difference equations x n+1 = x n−14 ±1 ± x n−2 x n−5 x n−8 x n−11 x n−14 , n = 0, 1, 2,. .. , where the initial conditions x −14 , x −13 ,. .. , x 0 are arbitrary real numbers. Moreover, we investigate stability, boundedness, oscillation and the periodic character of these solutions. Finally, we confirm the results with some numerical examples and graphs by using Matlab program.

Research paper thumbnail of Global behavior of a third-order rational difference equation

The journal of mathematics and computer science, Jul 3, 2021

In this paper, we investigate the behavior of solutions of the difference equation x n+1 = α (x n... more In this paper, we investigate the behavior of solutions of the difference equation x n+1 = α (x n−1 + x n−2) + (α − 1) x n−1 x n−2 x n−1 x n−2 + α , n = 0, 1, 2,. .. , where the initial conditions x −2 , x −1 , x 0 are arbitrary non-negative real numbers and the parameter α ∈ [1, ∞). More precisely, we study the boundedness, stability, and oscillation of the solutions of this equation.

Research paper thumbnail of On (N,M)-a-normal And (N, M)-a-quasinormal Semi- Hilbert Space Operators

arXiv (Cornell University), Dec 4, 2019

The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian sp... more The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product h | k A := Ah | k h, k ∈ H induces a semi-norm. A. This makes H into a semi-Hilbertian space. An operator T ∈ B A

Research paper thumbnail of On <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span>-$A$-normal and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span>-$A$-quasinormal semi-Hilbertian space operators

Mathematica Bohemica

We obtain some new sufficient conditions for the oscillation of the solutions of the second-order... more We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known ones.

Research paper thumbnail of Global behavior of a third-order rational difference equation

Journal of Mathematics and Computer Science, 2021

In this paper, we investigate the behavior of solutions of the difference equation x n+1 = α (x n... more In this paper, we investigate the behavior of solutions of the difference equation x n+1 = α (x n−1 + x n−2) + (α − 1) x n−1 x n−2 x n−1 x n−2 + α , n = 0, 1, 2,. .. , where the initial conditions x −2 , x −1 , x 0 are arbitrary non-negative real numbers and the parameter α ∈ [1, ∞). More precisely, we study the boundedness, stability, and oscillation of the solutions of this equation.

Research paper thumbnail of Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenth-order

Journal of Mathematics and Computer Science, 2021

The main goal of this paper, is to obtain the forms of the solutions of the following nonlinear f... more The main goal of this paper, is to obtain the forms of the solutions of the following nonlinear fifteenth-order difference equations x n+1 = x n−14 ±1 ± x n−2 x n−5 x n−8 x n−11 x n−14 , n = 0, 1, 2,. .. , where the initial conditions x −14 , x −13 ,. .. , x 0 are arbitrary real numbers. Moreover, we investigate stability, boundedness, oscillation and the periodic character of these solutions. Finally, we confirm the results with some numerical examples and graphs by using Matlab program.