In this article, we study ruled surfaces in a Lorentz-Minkowski space, which has finite type immersion. We give a complete classification of ruled surfaces of finite type immersion into a Lorentz-Minkowski space with arbitrary codimension.

If $X$ is a discrete topological space, the points of its Stone-Čech compactification $\beta X$ can be regarded as ultrafilters on $X$, and this fact is a useful tool in analysing the properties of $\beta X$. The purpose of this paper is to describe the compactification $\tilde{X}$ of a metric space in terms of the concept of near ultrafilters. We describe the topological space $\tilde{X}$ and we investigate conditions under which $\tilde{S}$ will be a semigroup compactification if $S$ is a semigroup which has a metric. These conditions will always hold if the topology of $S$ is defined by an invariant metric, and in this case our compactification $\tilde{S}$ coincides with $S^{LUC}$.

In this paper, we establish some weak and strong convergence theorems of modified Ishikawa iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [2], Osilike and Aniagbosor [10], Rhoades [11] and Schu [13, 14] and others.

Let $V_n(q)$ be the $n$-dimensional vector space over the finite field with $q$ elements and $K$ a selected $k$-dimensional subspace of $V_n(q)$. Let $C[n,k,t]$ denote the set of all subspaces $S$’s such that $\dim (S \cap K) \geq t$. We show that $C[n,k,t]$ has the normalized matching property, which yields that $C[n,k,t]$ has the strong Sperner property and the LYM property.

Let $R$ be a 2-torsionfree ring with identity and $S$ be a subring of the ring $M_n(R)$ that contains the ring $T_n(R)$ of all upper triangular matrices over $R$; that is, $T_n(R) \subseteq S \subseteq M_n(R)$. The goal of this paper is to describe a Jordan derivation $\Delta$ on $S$. The main result states that $\Delta$ can be uniquely represented as the sum of a derivation and a very special Jordan derivation. This result describes also the structure of every derivation on the ring $S$ which is an extension of a result of S.P. Coelho and C.P. Milies and a result of $S$. Jøndrup. Moreover, one of the corollaries of the main theorem covers the classical result by Jacobson and Rickart stating that there are no proper Jordan derivations on $M_n(R)$, and a more recent result by D. Benkovic that there are no proper Jordan derivations on the algebra $T_n(R)$.

A monotonic nondecreasing mapping connected with Hadamard type inequalities in two variables is given and some Hadamard type inequalities for Lipschizian mapping in two variables are established.

Through the works of many, now it is well known that the existence of dilation to the direct sum of a weighted shift is guaranteed by a positivity condition and a convergence condition. But the uniqueness of dilation is still not well understood.

In this paper we show that a theory of canonical operator models, not just the existence of dilation, can be achieved for general weighted shifts, with a level of sophistication at least close to that for the d-shifts on the symmetric Fock spaces.

Most techniques used in the paper are known, but we do have new ingredients which give a clearer picture even on the symmetric Fock space, where a nice theory has been developed by Arveson.

We give some new generalized $R$-KKM theorems in the nonconvexity setting of topological spaces. As an application we answer a question posed by Isac et al. for the lower and upper bounds equilibrium problem in topological spaces.

In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in Alg$\mathcal{L}$-module $\mathcal{U}_{\phi}$ is initiated, where $\mathcal{L}$ is a completely distributive subspace lattice on a Banach space $\mathcal{X}$ and $\phi$ is an order homomorphism from $\mathcal{L}$ into $\mathcal{L}$. For a reflexive Banach space $\mathcal{X}$ and a positive integer $n$ (or $+\infty$), by virtue of the order homomorphism $\phi$ we give necessary and sufficient conditions for the existence of single elements of $\mathcal{U}_{\phi}$ of rank $n$ (or $+\infty$).

In this paper we present the notion of regularized resolvent families, which generalizes the classes of regularized semigroups, regularized cosine families and resolvent families. We obtained some generation theorems and analyticity criterions for regularized resolvent families.

The main result presented in this paper is the existence of a nontrivial subspace of an $\mathcal{A}$-module Banach space $X$ hyperinvariant for the commutative algebra $\mathcal{A}$. From this result we can deduce the 1952 theorem of J. Wermer [8] and some other classical results on the existence of a nontrivial invariant subspace.

In this paper every $b$-weakly compact operator is shown to factor through a $KB$-space. Also we give some necessary and sufficient conditions for a continuous operator $T : E \to X$ from a Banach lattice into a Banach space to be a $b$-weakly compact. Moreover, we investigated the order structure of $b$-weakly compact operator.

In this paper we are interested in the problem of multipliers for the intersection of weighted $L^p(G)$-spaces. We prove theorem by the different characterization of multipliers, which include the results of Murthy and Unni(1973) as particular case.

In this paper we give the direct, inverse and equivalence theorem for Baskakov-Kantorovich-Bézier operators in the space $L_p[0,\infty)$ ($1 \leq p \leq \infty$) with Ditzian-Totik modulus.

In this paper we prove that every planar graph $G$ is 3-choosable if it contains no cycle of length at most 10 with a chord. This generalizes a result obtained by Borodin [J. Graph Theory 21(1996) 183-186] and Sanders and Zhao [Graphs Combin. 11(1995) 91-94], which says that every planar graph $G$ without $k$-cycles for all $4 \leq k \leq 9$ is 3-colorable.

Using the Darbo’s fixed-point theorem associated with the measure of noncompactness due to Banaś, we establish the existence and asymptotic stability of solutions for a functional-integral equation. An example which shows the importance of our result is also included.

In this paper, we classify ruled surfaces in Lorentz-Minkowski 3-spaces satisfying some algebraic equations in terms of the second Gaussian curvature, the mean curvature and the Gaussian curvature.

Let $G$ be a Lie group and $H$ its subgroup, and let $M^p$, $N^q$ be two submanifolds of dimensions $p$, $q$, respectively, in the Riemannian homogeneous space $G/H$. We study the relationships between the second fundamental forms of $M^p \cap gN^q$ and the second fundamental forms of $M^p$, $N^q$ for $g \in G$. We find that the second fundamental form of $M^p \cap gN^q$ can be expressed by the curvature functions of $M^p$, $N^q$ and the “angle” between $M^p$ and $N^q$. All results achieved are the generalizations of known results of the classical differential geometry in $\mathrm{R}^3$.

In this article, the logarithmic convexity of the one-parameter mean values $J(r)$ and the monotonicity of the product $J(r) J(−r)$ with $r \in \mathbb{R}$ are presented. Some more general results are established.

The convergence of the King-Werner method for finding zeros of nonlinear operators is analyzed. Under the hypothesis that the derivative of $f$ satisfies the radius Lipschitz condition with $L$-average, the convergence criterion and the convergence ball for the King-Werner method are given. Applying the results to some particular functions $L(u)$, we get the convergence theorems in [7] and [1] as well as some new results.

In this paper identities related to derivations and centralizers on operator algebras are considered. We prove the following result which is related to a classical result of Chernoff. Let $X$ be a real or complex Banach space, let $L(X)$ and $F(X)$ be the algebra of all bounded linear operators and the ideal of all finite rank operators on $X$, respectively. Suppose there exist linear mappings $D,G : F(X) \to L(X)$ such that $D(A^2) = D(A)A + AG(A)$ and $G(A^2) = G(A)A + AD(A)$ is fulfilled for all $A \in F(X)$. In this case there exists $B \in L(X)$ such that $D(A) = G(A) = [A,B]$ holds for all $A \in F(X)$.

In this paper, we study $p.q.$-Baer modules and some polynomial extensions of $p.q.$-Baer modules. In particular, we show: (1) For a reduced module $M_R$, $M_R$ is a $p.p.$-module iff $M_R$ is a $p.q.$-Baer module. (2) If $M_R$ is an $\alpha$-reduced module where $\alpha$ is an endomorphism of $R$, then $M_R$ is a $p.q.$-Baer module iff $M[x;\alpha]_{R[x;\alpha]}$ is a $p.q.$-Baer module. (3) For an arbitrary module $M_R$, $M_R$ is a $p.q.$-Baer module if and only if $M[x]_{R[x]}$ is a $p.q.$-Baer module.

In the present paper, we investigate the situations so that the generalized Hyers-Ulam-Rassias stability for functional equations $f(x^2) = f(x)x + xf(x)$ and $f(xy) = f(x)y + xf(y)$ is satisfied. As a result we obtain that every linear mapping on a commutative Banach algebra which is an $\varepsilon$-approximate derivation maps the algebra into its radical.