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M. Aslam Noor,Khalida Inayat Noor,Syed Tauseef Mohyud-Din,Noor Ahmed Shaikh 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods. In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.
Noor, Muhammad Aslam,Noor, Khalida Inayat,Mohyud-Din, Syed Tauseef,Shaikh, Noor Ahmed The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.
Noor, Khalida Inayat,Murtaza, Rashid,Sokol, Janusz Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.1
In this article the Srivastava-Owa-Ruscheweyh fractional derivative operator $\mathcal{L}^{\alpha}_{a,{\lambda}}$ is applied for defining and studying some new subclasses of analytic functions in the unit disk E. Inclusion results, radius problem and other results related to Bernardi integral operator are also discussed. Some applications related to conic domains are given.
HIGHER ORDER CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH RUSCHEWEYH DERIVATIVE OPERATOR
NOOR, KHALIDA INAYAT,SHAH, SHUJAAT ALI The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.1
The purpose of this paper is to introduce and study certain subclasses of analytic functions by using Ruscheweyh derivative operator. We discuss various of interesting properties such as, necessary condition, arc length problem and growth rate of coefficient of newly defined class. Also rate of growth of Hankel determinant will be estimated.
ON A CLASS OF QUANTUM ALPHA-CONVEX FUNCTIONS
KHALIDA INAYAT NOOR,RIZWAN S. BADAR 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.5
Let f : f(z) = z + Σ∞ n=2 anzn be analytic in the open unit disc E: Then f is said to belong to the class M of alpha-convex functions, if it satisfies the condition ℜ { (1 − ) zf′(z) f(z) + (zf′(z))′ f′(z) } > 0; (z ∈ E): In this paper, we introduce and study q-analogue of the class M by using concepts of Quantum Analysis. It is shown that the functions in this new class M(q; ) are q-starlike. A problem related to q-Bernardi operator is also investigated.
ON A CLASS OF QUANTUM ALPHA-CONVEX FUNCTIONS
NOOR, KHALIDA INAYAT,BADAR, RIZWAN S. The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.5
Let $f:f(z)=z+{\sum^{{\infty}}_{n=2}}a_nz^n$ be analytic in the open unit disc E. Then f is said to belong to the class $M_{\alpha}$ of alpha-convex functions, if it satisfies the condition ${\Re}\{(1-{{\alpha})}{\frac{zf^{\prime}(z)}{f(z)}}+{{\alpha}}{\frac{(zf^{\prime}(z))^{\prime})}{f^{\prime}(z)}}\}$ > 0, ($z{\in}E$). In this paper, we introduce and study q-analogue of the class $M_{\alpha}$ by using concepts of Quantum Analysis. It is shown that the functions in this new class $M(q,{\alpha})$ are q-starlike. A problem related to q-Bernardi operator is also investigated.
Applications of Convolution Operators to some Classes of Close-to-convex Functions
Noor, Khalida Inayat 호남수학회 1988 호남수학학술지 Vol.10 No.1
Let C[C,D] and S^*[C,D] denote the classes of functions g. g(0)=1-g'(0)0=0, analytic in the unit disc E such that (zg′(z))′/g′(z) and zg′(z)/g(z) are subordinate to 1+Cz/1+Dz′z∈E, respectively. In this paper, the classes K[A,B;C,D] and C^*[A,B;C,D], -1≤B$lt;A≤1; -1≤D$lt;C≤1, are defined. The functions in these classes are close-to-convex. Using the properties of convolution operators, we deal with some problems fur our classes.
Generalized Close-To-Convex Functions
Noor, Khalida Inayat 호남수학회 1995 호남수학학술지 Vol.17 No.1
We introduce a new class of analytic functions in the unit disk which generalizes the concepts of close-to-convexity and of bounded boundary rotation, and study its various properties including its connection with other classes of analytic and univalent functions.
Some Properties of Certain Classes of Functions With Bounded Radius Rotations
Noor, Khalida Inayat 호남수학회 1997 호남수학학술지 Vol.19 No.1
Let R_k(a), 0≤α$lt;1, k≥2 denote certain subclasses of analytic functions in the unit disc E with bounded radius rotation. A function f , analytic in E and given by ※수식※, is said to be in the family R_k(n,α)n∈N_o={0,1,2,...} and * denotes the Hadamard product. The classes R_k(n,α) are investigated and same properties are given. It is shown that R_k(n+1,α)⊂R_k(n,α) for each n. Same integral operators defined on R_k(n,α) are also studied.
On A Class of Univalent Functions
Noor, Khalida Inayat,Ramadan, Fatma H . 호남수학회 1993 호남수학학술지 Vol.15 No.1
For A and B, -1≤B$lt;A≤1, let P[A,B] he the class of functions p analytic in the unit disk E with P(0)=1 and subordinate to 1+Az/1+Bz. We introduce the class T_α[A,B] of functions ※수식※ which are analytic in E and for z∈E, α≥0, ※수식※. It is shown that, far α≥1, T_α[A,B] consists entirely of univalent functions and the radius of univalence for f∈T_α[A,B], 0$lt;α$lt;1 is obtained. Coefficient bounds and some other properties of this class are studied. Some radii problems are also solved.