Iranian Journal of Mathematical Sciences and Informatics
Year:2017 | Volume:12 | Issue:2|Papers Count:8

In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane–Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first linearize the equation using quasilinearization technique and solve the resulting problem by a third degree B-spline function. Some numerical examples are included to demonstrate the feasibility and the efficiency of the proposed technique. The method is easy to implement and produces accurate results. The numerical results are also found to be in good agreement with the exact solutions.

In this paper, we introduce the concept of Krasner hyperring (R,+,.) together with a suitable partial order relation £. Also, we con-sider some Krasner hyperrings and dene a binary relation on them which become ordered Krasner hyperrings. By using the notion of pseudoorder on an ordered Krasner hyperring (R,+,.,£), we obtain an ordered ring. Moreover, we give some results on ordered Krasner hyperrings.

By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

In this work, we have presented some iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monotone operators.

The paper presents an Lr− analogue of an inequality regarding the sth derivative of a polynomial having zeros outside a circle of arbitrary radius but greater or equal to one. Our result provides improvements and generalizations of some well-known polynomial inequalities.

In this work, applying a lemma due to Nunokawa et al. (J. Ineq. Appl. 2015. 1 (2015)  7), we obtain some sufficient inequalities for some certain subclasses of univalent functions.

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem forP-valued functions and operator valued measure q: ®L (P, Q), where R is a s-ring of subsets of X¹q, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally convex complete lattice cone.

Let R be a prime ring with its Utumi ring of quotients U, C=Z (U) the extended centroid of R, L a non-central Lie ideal of R and 0 ¹aÎR. If R admits a generalized derivation F such that a (F (u2)±F(u) 2) =0 for all uÎL, then one of the following holds: (1) there exists bÎU such that F (x) =bx for all xÎR, with ab=0;(2)F (x)=±x for all xÎR; (3) char (R)=2 and R satisfies s4; (4) char (R)¹2, R satisfies s4 and there exists bÎU such that F (x) = bx for all xÎR.We also study the situations (i)a (F (xmyn)±F (xm) F (yn)) =0 for all x, yÎR, and (ii) a (F (xmyn)±F (yn) F (xm))=0 for all x, y ÎR in prime and semiprime rings.