Iranian Journal of Mathematical Sciences and Informatics
Volume:10 Issue: 2, Nov 2015

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then the solution of the discretized form is approximated by an iterative scheme. Comparison of the approximate solution with exact solution shows that the used approach is easy and practical for some classes of linear and nonlinear Volterra-Fredholm integral equations.

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are Lipschitz near the optimal solution. Necessary optimality conditions and constraint qualifications in terms of Michel-Penot subdifferential are given.

In this paper we will generalize a singular value inequality that was proved before. In particular we obtain an inequality for numerical radius as follows: begin{equation*} 2 sqrt{t (1-t)} omega(t A^{nu}B^{1-nu}+(1-t)A^{1-nu}B^{nu}) leq omega(t A + (1- t) B), end{equation*} where, $ A $ and $ B $ are positive semidefinite matrices, $ 0 leq t leq 1 $ and $ 0 leq nu leq frac{3}{2}.$

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-modules, we give a method to make a free object on a nonempty set and in BCK-algebra of order 2, we give a method to make a basis for unitary extended BCK-modules. Finally, we define the notions of projective and productive modules and we investigate the relation between free modules and projective modules. In special case, we state the relation between free modules and productive modules.

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F: R! R is called a generalized derivation on R if there exists a derivation d: R to R such that F(xy) = F(x)y + xd(y) holds for all x; y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.

In this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups. We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.

In this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (α, β)-metric with vanishing S-curvature reduce to the class of Berwald metrics.

By the Mordell - Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves, where p and q are distinct primes. We give infinite families of elliptic curves of the form y2=x3-pqx with rank two, three and four, assuming a conjecture of Schinzel and Sierpinski is true.

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1,. .. , mr−1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are computed.

In this paper, we introduce a new class of (semi) hypergroup from a given (partially) quasi-ordered (semi) hypergroup as a generalization of {it «$El$–hyperstructures»}. Then, we study some basic properties and important elements belong to this class.}

The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the graph $G$ considered has maximum diameter, the complexity is improved to $mathcal O (|V(G)|cdot |E(G)|+Delta(G)^3)$.