Caspian Journal of Mathematical Sciences
Volume:1 Issue: 2, Summer Autumn 2012

In this paper, after reviewing some results in minimal space, some new results in this setting are given. We prove a generalized form of the Fan-KKM type
theorem in minimal vector spaces. As some applications, the open type of matching theorem and generalized form of the classical KKM theorem in minimal vector spaces are given.

The main purpose of this paper is to establish some new results on the superstability and stability via a fixed point approach for the Pexiderized exponential equation, i.e., $$|f(x+y)-g(x)h(y)|leq psi(x,y),$$ where $f$, $g$ and $h$ are three functions from an arbitrary commutative semigroup $S$ to an arbitrary unitary complex Banach algebra and also $psi: S^{2}rightarrow [0,infty)$ is a function. Furthermore, in connection with the open problem of Th. M. Rassias and our results we generalized the theorem of Baker, Lawrence, Zorzitto and theorem of L. Sz$acute{e}$kelyhidi.

In this paper  we give new results on the best approximation  in the Hausdorff topological vector space and  consider relationship  with orthogonality. Also we determined under  what  conditions the map $P_{K,f}$ is upper semicontinous.

This paper is devoted to the proof of the unique solvability of the inverse problems for second-order differential operators with regular singularities. It is shown that the potential function can be determined from spectral data, also we prove a uniqueness theorem in the inverse problem.

This paper studies the Biswas-Milovic equation with log law nonlinearity. The Gausson solution is obtained by the ansatz method. Subsequently, the conservation laws are derived and the conserved quantities are computed using the Gausson solution.

In this paper, we are supposed to introduce the definitions of n-fold commutative, and implicative hyper K-ideals. These definitions are the generalizations of the definitions of commutative, and implicative hyper K-ideals, respectively, which have been defined in [12]. Then we obtain some related results. In particular we determine the relationships between n-fold implicative hyper K-ideal and n-fold commutative hyper K-ideals of a hyper K-algebra of order 3, which satisfy the simple condition. Then, generally we study n-fold commutative hyper K-ideals in simple hyper K-algebras.

This comment is to show that Theorem 3.3 of Dey and Chung (1991) (Multiparameter estimation in truncated power series distributions under the Stein's loss. emph{Commun. Statist.-Theory Meth.,} {bf 20}, 309-326) may give us misleading results. Analytically and through simulation, we show that the Theorem does not improve the given estimator.

In this paper we obtain  exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes many physical processes in motion of turbulence and other unstable process systems.    The methods used  to determine the exact solutions of the underlying equation are the Lie group analysis  and the simplest equation method. The solutions obtained are  then plotted.