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 . 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&#039;hidi University, Oum El Bouaghi, Algeria. Département de Mathématiques et Informatique, Université Larbi Ben M&#039;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