2018
4
2
2
104
Accurate Numerical Method for Singularly Perturbed DifferentialDifference Equations with Mixed Shifts
2
2
This paper is concerned with the numerical solution of the singularly perturbed differentialdifference 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 differentialdifference equations with mixed shifts. The delay and advanced shifts are managed by Taylor series and an asymptotically equivalent singularly perturbed twopoint 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.
1

110
122


Diddi
Kumara Swamy
Department of Mathematics, Christu Jyoti Institute of Technology and
Science, Jangaon, 506167, India.
Department of Mathematics, Christu Jyoti
India
diddi.k@gmail.com


Kolloju
Phaneendra
Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, 500004,India.
Department of Mathematics, University College
India
kollojuphaneendra@yahoo.co.in


Y.N.
Reddy
Department of Mathematics, National Institute of Technology, Warangal,
506004, India.
Department of Mathematics, National Institute
India
ynreddy@nitw.ac.in
Singularly perturbed differentialdifference equation
Fitting factor
Boundary Layer
Tridiagonal system
Truncation error
On Certain Results Involving a Multiplier Transformation in a Parabolic Region
2
2
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, closetoconvexity and uniform closetoconvexity of pvalent analytic functions as well as univalent analytic functions.
1

123
143


Richa
Brar
Department of Mathematics, Sri Guru Granth Sahib World University ,
Fatehgarh Sahib140407, Punjab, India.
Department of Mathematics, Sri Guru Granth
India
richabrar4@gmail.com


Sukhwinder
Billing
Department of Mathematics, Sri Guru Granth Sahib World University ,
Fatehgarh Sahib140407, Punjab, India.
Department of Mathematics, Sri Guru Granth
India
ssbilling@gmail.com
Analytic function
parabolic starlike function
uniformly convex function
differential subordination
multiplier transformation
More on Convergence Theory of Proper Multisplittings
2
2
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.
1

144
154


Chinmay
Giri
Department of Mathematics, National Institute of Technology Raipur, Raipur
492010, Chhattisgarh, India.
Department of Mathematics, National Institute
India
ckg2357@gmail.com


Debasisha
Mishra
Department of Mathematics, National Institute of Technology Raipur, Raipur
492010, Chhattisgarh, India.
Department of Mathematics, National Institute
India
dmishra@nitrr.ac.in
MoorePenrose inverse
proper splitting
multisplittings
convergence theorem
comparison theorem
Uniqueness of Meromorphic Functions with Regard to Multiplicity
2
2
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].
1

155
166


Harina
Waghamore
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru560056, INDIA
Department of Mathematics, Jnanabharathi
India
harinapw@gmail.com


Naveenkumar
Sannappala
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru560056, INDIA
Department of Mathematics, Jnanabharathi
India
naveenkumarsh.220@gmail.com
uniqueness
meromorphic function
differential polynomial
multiplicity
Expanding the Applicability of Generalized High Convergence Order Methods for Solving Equations
2
2
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 Lipschitztype conditions, which is not given in earlier studies. Numerical examples conclude this study.
1

167
177


Ioannis K
Argyros
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA.
Department of Mathematical Sciences, Cameron
United States
iargyros@cameron.edu


Santhosh
George
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India575 025.
Department of Mathematical and Computational
India
sgeorge@nitk.ac.in
Three step method
local convergence
Fr'echet derivative
system of equations
Banach space
Generalized Ricci Solitons on TransSasakian Manifolds
2
2
The object of the present research is to shows that a transSasakian manifold, which also satisfies the Ricci soliton and generalized Ricci soliton equation, satisfying some conditions, is necessarily the Einstein manifold.
1

178
186


Mohd
Siddiqi
Department of Mathematics, Jazan University, Faculty of Science, Jazan,
Kingdom of Saudi Arabia.
Department of Mathematics, Jazan University,
Saudi Arabia
anallintegral@gmail.com
Generalized Ricci Solitons
transSasakian manifold
Einstein manifold
On a New Subclass of mFold Symmetric Biunivalent Functions Equipped with Subordinate Conditions
2
2
In this paper, we introduce a new subclass of biunivalent function class $Sigma$ in which both $f(z)$ and $f^{1}(z)$ are mfold 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 FeketeSzegö functional estimate for this class. Consequences of the results are also discussed.
1

187
197


Emeka
Mazi
Department of Mathematics, Faculty of Science, University of Ilorin, Nigeria
Department of Mathematics, Faculty of Science,
Nigeria
emekmazi21@gmail.com


Şahsene
Altinkaya
Department of Mathematics, Faculty of Science, Uludag University, 16059,
Bursa, Turkey.
Department of Mathematics, Faculty of Science,
Turkey
sahsene@uludag.edu.tr
Biunivalent functions
coefficient bounds
pseudostarlike functions
FeketeSzegö functional estimates
TaylorMaclaurin coefficients
subordination
Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition
2
2
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.
1

198
213


Taki Eddine
Oussaeif
Department of Mathematics and Informatics., The Larbi Ben M'hidi
University, Oum El Bouaghi, Algeria.
Department of Mathematics and Informatics.,
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.
Département de Mathématiques
Algeria
aefbouziani@yahoo.fr
Energy inequality
Goursat equation
nonlinear hyperbolic problems
integral condition
a priori estimate