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 are<br />tabulated 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 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 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 . 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 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 http://www.kjm-math.org/article_65161.html http://www.kjm-math.org/article_65161_8fed2a0e71a8af7d76b734e82401f3b2.pdf