eng
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
2423-4788
2018-07-01
4
2
110
122
10.22034/kjm.2018.57949
57949
Accurate Numerical Method for Singularly Perturbed Differential-Difference Equations with Mixed Shifts
Diddi Kumara Swamy
diddi.k@gmail.com
1
Kolloju Phaneendra
kollojuphaneendra@yahoo.co.in
2
Y.N. Reddy
ynreddy@nitw.ac.in
3
Department of Mathematics, Christu Jyoti Institute of Technology and Science, Jangaon, 506167, India.
Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, 500004,India.
Department of Mathematics, National Institute of Technology, Warangal, 506004, India.
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.
http://www.kjm-math.org/article_57949_faad09b64d50416a8548558290d7ffba.pdf
Singularly perturbed differential-difference equation
Fitting factor
Boundary Layer
Tridiagonal system
Truncation error
eng
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
2423-4788
2018-07-01
4
2
123
143
10.22034/kjm.2018.59751
60177
On Certain Results Involving a Multiplier Transformation in a Parabolic Region
Richa Brar
richabrar4@gmail.com
1
Sukhwinder Billing
ssbilling@gmail.com
2
Department of Mathematics, Sri Guru Granth Sahib World University , Fatehgarh Sahib-140407, Punjab, India.
Department of Mathematics, Sri Guru Granth Sahib World University , Fatehgarh Sahib-140407, Punjab, India.
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.
http://www.kjm-math.org/article_60177_7ab19b219bbfb0fdfc4ef62533b63751.pdf
Analytic function
parabolic starlike function
uniformly convex function
differential subordination
multiplier transformation
eng
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
2423-4788
2018-07-01
4
2
144
154
10.22034/kjm.2018.60178
60178
More on Convergence Theory of Proper Multisplittings
Chinmay Giri
ckg2357@gmail.com
1
Debasisha Mishra
dmishra@nitrr.ac.in
2
Department of Mathematics, National Institute of Technology Raipur, Raipur 492010, Chhattisgarh, India.
Department of Mathematics, National Institute of Technology Raipur, Raipur 492010, Chhattisgarh, India.
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.
http://www.kjm-math.org/article_60178_45b35ce601f0a41c767c604a5ff62498.pdf
Moore-Penrose inverse
proper splitting
multisplittings
convergence theorem
comparison theorem
eng
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
2423-4788
2018-07-01
4
2
155
166
10.22034/kjm.2018.60179
60179
Uniqueness of Meromorphic Functions with Regard to Multiplicity
Harina Waghamore
harinapw@gmail.com
1
Naveenkumar Sannappala
naveenkumarsh.220@gmail.com
2
Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru-560056, INDIA
Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru-560056, INDIA
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].
http://www.kjm-math.org/article_60179_60795f61bcd501613831c381bf36238c.pdf
uniqueness
meromorphic function
differential polynomial
multiplicity
eng
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
2423-4788
2018-07-01
4
2
167
177
10.22034/kjm.2018.63368
63368
Expanding the Applicability of Generalized High Convergence Order Methods for Solving Equations
Ioannis K Argyros
iargyros@cameron.edu
1
Santhosh George
sgeorge@nitk.ac.in
2
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.
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.
http://www.kjm-math.org/article_63368_012c2c785e1430a9ff18422feb561db6.pdf
Three step method
local convergence
Fr'echet derivative
system of equations
Banach space
eng
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
2423-4788
2018-07-01
4
2
178
186
10.22034/kjm.2018.63446
63446
Generalized Ricci Solitons on Trans-Sasakian Manifolds
Mohd Siddiqi
anallintegral@gmail.com
1
Department of Mathematics, Jazan University, Faculty of Science, Jazan, Kingdom of Saudi Arabia.
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.
http://www.kjm-math.org/article_63446_eabee94b9a3fd4c91d2e2429b5763ac2.pdf
Generalized Ricci Solitons
trans-Sasakian manifold
Einstein manifold
eng
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
2423-4788
2018-07-01
4
2
187
197
10.22034/kjm.2018.63470
63470
On a New Subclass of m-Fold Symmetric Biunivalent Functions Equipped with Subordinate Conditions
Emeka Mazi
emekmazi21@gmail.com
1
Şahsene Altinkaya
sahsene@uludag.edu.tr
2
Department of Mathematics, Faculty of Science, University of Ilorin, Nigeria
Department of Mathematics, Faculty of Science, Uludag University, 16059, Bursa, Turkey.
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.
http://www.kjm-math.org/article_63470_def95421626bd10dbaaaf7b380ff11dd.pdf
Biunivalent functions
coefficient bounds
pseudo-starlike functions
Fekete-Szegö functional estimates
Taylor-Maclaurin coefficients
subordination
eng
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
2423-4788
2018-07-01
4
2
198
213
10.22034/kjm.2018.65161
65161
Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition
Taki Eddine Oussaeif
taki_maths@live.fr
1
Abdelfatah Bouziani
aefbouziani@yahoo.fr
2
Department of Mathematics and Informatics., The Larbi Ben M'hidi University, Oum El Bouaghi, Algeria.
Département de Mathématiques et Informatique, Université Larbi Ben M'hidi, Oum El Bouagui, B.P. 565, 04000, Algerie.
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.
http://www.kjm-math.org/article_65161_8fed2a0e71a8af7d76b734e82401f3b2.pdf
Energy inequality
Goursat equation
nonlinear hyperbolic problems
integral condition
a priori estimate