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
4
2
2018
07
01
Accurate Numerical Method for Singularly Perturbed Differential-Difference Equations with Mixed Shifts
110
122
EN
Diddi
Kumara Swamy
Department of Mathematics, Christu Jyoti Institute of Technology and
Science, Jangaon, 506167, India.
diddi.k@gmail.com
Kolloju
Phaneendra
Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, 500004,India.
kollojuphaneendra@yahoo.co.in
Y.N.
Reddy
Department of Mathematics, National Institute of Technology, Warangal,
506004, India.
ynreddy@nitw.ac.in
10.22034/kjm.2018.57949
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 aretabulated to illustrate the proposed method.
Singularly perturbed differential-difference equation,Fitting factor,Boundary Layer,Tridiagonal system,Truncation error
http://www.kjm-math.org/article_57949.html
http://www.kjm-math.org/article_57949_faad09b64d50416a8548558290d7ffba.pdf
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
4
2
2018
07
01
On Certain Results Involving a Multiplier Transformation in a Parabolic Region
123
143
EN
Richa
Brar
Department of Mathematics, Sri Guru Granth Sahib World University ,
Fatehgarh Sahib-140407, Punjab, India.
richabrar4@gmail.com
Sukhwinder
Singh
Billing
Department of Mathematics, Sri Guru Granth Sahib World University ,
Fatehgarh Sahib-140407, Punjab, India.
ssbilling@gmail.com
10.22034/kjm.2018.59751
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
http://www.kjm-math.org/article_60177.html
http://www.kjm-math.org/article_60177_7ab19b219bbfb0fdfc4ef62533b63751.pdf
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
4
2
2018
07
01
More on Convergence Theory of Proper Multisplittings
144
154
EN
Chinmay
Kumar
Giri
Department of Mathematics, National Institute of Technology Raipur, Raipur
492010, Chhattisgarh, India.
ckg2357@gmail.com
Debasisha
Mishra
Department of Mathematics, National Institute of Technology Raipur, Raipur
492010, Chhattisgarh, India.
dmishra@nitrr.ac.in
10.22034/kjm.2018.60178
In this paper, we first prove a few comparison results between twoproper weak regular splittings which are useful in getting theiterative solution of a large class of rectangular (square singular)linear system of equations $Ax = b$, in a faster way. We then deriveconvergence and comparison results for proper weak regularmultisplittings.
Moore-Penrose inverse,proper splitting,multisplittings,convergence theorem,comparison theorem
http://www.kjm-math.org/article_60178.html
http://www.kjm-math.org/article_60178_45b35ce601f0a41c767c604a5ff62498.pdf
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
4
2
2018
07
01
Uniqueness of Meromorphic Functions with Regard to Multiplicity
155
166
EN
Harina
Pandit
Waghamore
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru-560056, INDIA
harinapw@gmail.com
Naveenkumar
Halappa
Sannappala
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru-560056, INDIA
naveenkumarsh.220@gmail.com
10.22034/kjm.2018.60179
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
http://www.kjm-math.org/article_60179.html
http://www.kjm-math.org/article_60179_60795f61bcd501613831c381bf36238c.pdf
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
4
2
2018
07
01
Expanding the Applicability of Generalized High Convergence Order Methods for Solving Equations
167
177
EN
Ioannis K
Argyros
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA.
iargyros@cameron.edu
Santhosh
George
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.
sgeorge@nitk.ac.in
10.22034/kjm.2018.63368
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
http://www.kjm-math.org/article_63368.html
http://www.kjm-math.org/article_63368_012c2c785e1430a9ff18422feb561db6.pdf
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
4
2
2018
07
01
Generalized Ricci Solitons on Trans-Sasakian Manifolds
178
186
EN
Mohd
Danish
Siddiqi
Department of Mathematics, Jazan University, Faculty of Science, Jazan,
Kingdom of Saudi Arabia.
anallintegral@gmail.com
10.22034/kjm.2018.63446
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
http://www.kjm-math.org/article_63446.html
http://www.kjm-math.org/article_63446_eabee94b9a3fd4c91d2e2429b5763ac2.pdf
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
4
2
2018
07
01
On a New Subclass of m-Fold Symmetric Biunivalent Functions Equipped with Subordinate Conditions
187
197
EN
Emeka
Mazi
Department of Mathematics, Faculty of Science, University of Ilorin, Nigeria
emekmazi21@gmail.com
Şahsene
Altinkaya
Department of Mathematics, Faculty of Science, Uludag University, 16059,
Bursa, Turkey.
sahsene@uludag.edu.tr
10.22034/kjm.2018.63470
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
http://www.kjm-math.org/article_63470.html
http://www.kjm-math.org/article_63470_def95421626bd10dbaaaf7b380ff11dd.pdf
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
4
2
2018
07
01
Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition
198
213
EN
Taki Eddine
Oussaeif
Department of Mathematics and Informatics., The Larbi Ben M'hidi
University, Oum El Bouaghi, Algeria.
taki_maths@live.fr
Abdelfatah
Bouziani
Département de Mathématiques et Informatique, Université Larbi Ben M'hidi, Oum El Bouagui, B.P. 565, 04000, Algerie.
aefbouziani@yahoo.fr
10.22034/kjm.2018.65161
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 anduniqueness 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
http://www.kjm-math.org/article_65161.html
http://www.kjm-math.org/article_65161_8fed2a0e71a8af7d76b734e82401f3b2.pdf