2020-02-28T22:14:10Z
http://www.kjm-math.org/?_action=export&rf=summon&issue=8263
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
2
Accurate Numerical Method for Singularly Perturbed Differential-Difference Equations with Mixed Shifts
Diddi
Kumara Swamy
Kolloju
Phaneendra
Y.N.
Reddy
This paper is concerned with the numerical solution of the singularly perturbed differential-difference equations with small shifts called delay and advanced parameters. A fourth order finite difference method with a fitting factor is proposed for the solution of the singularly perturbed differential-difference equations with mixed shifts. The delay and advanced shifts are managed by Taylor series and an asymptotically equivalent singularly perturbed two-point boundary value problem is obtained. A fitting factor is introduced in the fourth order finite difference scheme for the problem which takes care of the small values of the perturbation parameter. This fitting factor is obtained from the asymptotic solution of singular perturbations. Thomas algorithm is used to solve the discrete system of the difference scheme. Convergence of the proposed method is analyzed. Maximum absolute errors in comparison with the several numerical experiments are<br />tabulated to illustrate the proposed method.
Singularly perturbed differential-difference equation
Fitting factor
Boundary Layer
Tridiagonal system
Truncation error
2018
07
01
110
122
http://www.kjm-math.org/article_57949_faad09b64d50416a8548558290d7ffba.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
2
On Certain Results Involving a Multiplier Transformation in a Parabolic Region
Richa
Brar
Sukhwinder
Billing
We, here, obtain certain results in subordination form involving a multiplier transformation in a parabolic region. In particular, using different dominants in our main result, we derive certain results on parabolic starlikeness, starlikeness, convexity, uniform convexity, strongly starlikeness, close-to-convexity and uniform close-to-convexity of p-valent analytic functions as well as univalent analytic functions.
Analytic function
parabolic starlike function
uniformly convex function
differential subordination
multiplier transformation
2018
07
01
123
143
http://www.kjm-math.org/article_60177_7ab19b219bbfb0fdfc4ef62533b63751.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
2
More on Convergence Theory of Proper Multisplittings
Chinmay
Giri
Debasisha
Mishra
In this paper, we first prove a few comparison results between two<br />proper weak regular splittings which are useful in getting the<br />iterative solution of a large class of rectangular (square singular)<br />linear system of equations $Ax = b$, in a faster way. We then derive<br />convergence and comparison results for proper weak regular<br />multisplittings.
Moore-Penrose inverse
proper splitting
multisplittings
convergence theorem
comparison theorem
2018
07
01
144
154
http://www.kjm-math.org/article_60178_45b35ce601f0a41c767c604a5ff62498.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
2
Uniqueness of Meromorphic Functions with Regard to Multiplicity
Harina
Waghamore
Naveenkumar
Sannappala
In this paper, we investigate the uniqueness problem on meromorphic functions concerning differential polynomials sharing one value. A uniqueness result which related to multiplicity of meromorphic function is proved in this paper. By using the notion of multilplicity our results will generalise and improve the result due to Chao Meng [10].
uniqueness
meromorphic function
differential polynomial
multiplicity
2018
07
01
155
166
http://www.kjm-math.org/article_60179_60795f61bcd501613831c381bf36238c.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
2
Expanding the Applicability of Generalized High Convergence Order Methods for Solving Equations
Ioannis K
Argyros
Santhosh
George
The local convergence analysis of iterative methods is important since it indicates the degree of difficulty for choosing initial points. In the present study we introduce generalized three step high order methods for solving nonlinear equations. The local convergence analysis is given using hypotheses only on the first derivative, which actually appears in the methods in contrast to earlier works using hypotheses on higher derivatives. This way we extend the applicability of these methods. The analysis includes computable radius of convergence as well as error bounds based on Lipschitz-type conditions, which is not given in earlier studies. Numerical examples conclude this study.
Three step method
local convergence
Fr'echet derivative
system of equations
Banach space
2018
07
01
167
177
http://www.kjm-math.org/article_63368_012c2c785e1430a9ff18422feb561db6.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
2
Generalized Ricci Solitons on Trans-Sasakian Manifolds
Mohd
Siddiqi
The object of the present research is to shows that a trans-Sasakian manifold, which also satisfies the Ricci soliton and generalized Ricci soliton equation, satisfying some conditions, is necessarily the Einstein manifold.
Generalized Ricci Solitons
trans-Sasakian manifold
Einstein manifold
2018
07
01
178
186
http://www.kjm-math.org/article_63446_eabee94b9a3fd4c91d2e2429b5763ac2.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
2
On a New Subclass of m-Fold Symmetric Biunivalent Functions Equipped with Subordinate Conditions
Emeka
Mazi
Şahsene
Altinkaya
In this paper, we introduce a new subclass of biunivalent function class $Sigma$ in which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric analytic functions. For functions of the subclass introduced in this paper, we obtain the coefficient bounds for $|a_{m+1}|$ and $|a_{2m+1}|$ and also study the Fekete-Szegö functional estimate for this class. Consequences of the results are also discussed.
Biunivalent functions
coefficient bounds
pseudo-starlike functions
Fekete-Szegö functional estimates
Taylor-Maclaurin coefficients
subordination
2018
07
01
187
197
http://www.kjm-math.org/article_63470_def95421626bd10dbaaaf7b380ff11dd.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
2
Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition
Taki Eddine
Oussaeif
Abdelfatah
Bouziani
This paper is concerned with the existence and uniqueness of a strong solution for linear problem by using a functional analysis method, which is based on an energy inequality and the density of the range of the operator generated by the problem. Applying an iterative process based on results obtained from the linear problem, we prove the existence and<br />uniqueness of the weak generalized solution of nonlinear hyperbolic Goursat problem with integral condition.
Energy inequality
Goursat equation
nonlinear hyperbolic problems
integral condition
a priori estimate
2018
07
01
198
213
http://www.kjm-math.org/article_65161_8fed2a0e71a8af7d76b734e82401f3b2.pdf