We present common fixed point theorems for a pair of weakly isotone increasing multivalued mappings satisfying general weak contractive conditions, as well as almost contractive conditions in ordered complete metric spaces. Examples are presented to show the usage of these results.

We describe a construction of a point-line presheaf on a point-line geometry from a set of presheaves on subspaces of the geometry. Then we combine our construction with theorems of M. Ronan to give a new proof of the fact that all polar spaces of finite rank at least four, and several other Grassmann geometries of spherical buildings, are embeddable in projective spaces.

The Riemannian wave equation with linear lower order term and unspecified behavior of the nonlinear feedback $f$ is considered. Using the method in $ \left[ LT\right] $ we prove that the energy of the solution decays faster than the solution of some associated differential equation. The decay rate of a general second order hyperbolic equation with polynomial growth at the origin of $f$ is also discussed.

It is shown that the assumption of the singularity of $\varphi$--Laplacian permits to get for the scalar differential equations the existence results of the Dirichlet, Dirichlet--Neumann, Neuman--Steklov or periodic problems using a simple elementary argument.

In the present paper we show that contractive condition employed by Al-Thagafi and Shahzad in particular and contractive conditions in general, do not constitute a proper setting for studying common fixed points of occasionally weakly compatible mappings. Further, we improve the results of Al-Thagafi and Shahzad by employing a proper setting.

By using unbounded modulus functions we introduce a new concept of density for sets of pairs of natural numbers. Consequently, we obtain a generalization of the notion of statistical convergence of double sequences which is studied and characterized. As an application, we prove that `Pringsheim convergence' is equivalent to `module statistical convergence for every unbounded modulus function'.

In this paper, we prove that if the positive part $u^{+}(x)$ of a harmonic function $u(x)$ in the upper half space satisfies a fast growing condition, then its negative part $u^{-}(x)$ can also be dominated by a similar growing condition. Meanwhile, $u(x)$ can be represented in terms of the modified Poisson integral and a harmonic function vanishing on the boundary.

In this article we define the continuous Gabor transform for second countable, non-abelian, unimodular and type I groups and also we investigate a Plancherel formula and an inversion formula for our definition. As an example we show that how these formulas work for the Heisenberg group and also the matrix group ${SL(2,\mathbb{R})}$.

The purpose of this paper is to discuss the deficiency of an E-valued meromorphic function $f$. Results are obtained to extend the related results for meromorphic vector valued function of Lahiri and Ziegler.

In this paper, we further investigate the exponent of convergence of the zero-sequence of solutions of the differential equation $$ f^{(k)}+a_{k-1}(z)f^{(k-1)}+\cdots+a_1(z)f' +\psi(z)f=0, $$ where $\psi(z)=\sum_{j=1}^\iota Q_j(z)e^{P_j(z)} (\iota\geq 3, \iota\in N_+ )$, $P_j(z)$ are polynomials of degree $n\geq1$, $Q_j(z),a_\Lambda(z)(\Lambda=1,2,\cdots,k-1;j=1,2,\ldots,\iota)$ are entire functions of order less than $n$, and $k\geq2$.

In this paper, the complete spacelike submanifold with parallel normalized mean curvature vector and constant normalized scalar curvature is discussed in $(n+p)$-dimensional connected semi-Riemannian manifold $S^{n+p}_q(1)$ $(1\leq q\leq p)$ and a rigidity theorem is obtained.

The existence of homoclinic solutions is obtained for a class of nonautonomous second order Hamiltonian systems $\ddot{u}(t)+\nabla V(t,u(t))=f(t)$ as the limit of the $2kT$-periodic solutions which are obtained by the Mountain Pass theorem, where $V(t,x)=-K(t,x)+W(t,x)$ is $T$-periodic with respect to $t,T>0$, and $W(t,x)$ satisfies the superquadratic condition: $W(t,x) / |x|^{2} \rightarrow +\infty$ as $|x| \rightarrow \infty$ uniformly in $t$, which needs not to satisfy the global Ambrosetti-Rabinowitz condition.

The object of the present paper is to derive the radius of convexity for certain multivalent functions with missing coefficients.