X. Qin and Y. Su proved a strong convergence theorems of modified Ishikawa iteration by CQ method for relatively nonexpansive mappings in a Banach space [Xiaolong Qin, Yongfu Su, Nonlinear Anal. 67 (2007), no. 6, 1958-1965]. The result of this paper extends and improves the result of X. Qin and Y. Su in the two respects: (1). By using the monotone CQ method to modify the CQ method, so that the new method of proof is used. (2). Relax the restriction on $T$ from uniformly continuous to continuous. The result of this paper also extends and improves the recent ones announced by Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others.

In this article we study the existence of non-continuous linear functionals on topological vector spaces. Both sufficient and necessary conditions for the existence of such maps are found.

Some new kinds of Hardy-Hilbert's integral inequality in which the weight function is homogeneous function are given. Other results are also obtained.

In this paper we solve the functional equation $$f\big(\alpha x+(1-\alpha)y\big)+f\big(\beta x+(1-\beta)y\big)= f\big(\gamma x+(1-\gamma)y\big)+f\big(\delta x+(1-\delta)y\big)$$ which holds for all $x, y\in I$, where $I\subset \mathbb{R}$ is a non-void open interval, $f\colon I\to \mathbb{R}$ is an unknown function and $\alpha,\beta,\gamma,\delta\in (0,1)$ are arbitrarily fixed.

In this paper, we use the auxiliary principle technique to study the existence of a solution of the extended general variational inequalities, which were introduced and studied by the author. Several special cases are also discussed.

The purpose of this work is to give different products of closed operators together with their faults and assets.

We apply the Luxemburg-Jung fixed point theorem in generalized metric spaces to study the Hyers-Ulam stability for two functional equations in a single variable.

We consider two general integral operators where are the extensions of the Kim-Merkes operator and Pfaltzgraff operator. We will proved in this paper the univalent conditions for these operators when we make some restrictions about the functions from your definitions.

In this paper, we prove the generalized Hyers-Ulam stability of the isometric additive mappings in generalized quasi-Banach spaces, and prove the generalized Hyers-Ulam stability of the isometric additive mappings in generalized $p$-Banach spaces.

The main purposes of this paper are to establish some new Brunn-Minkowski inequalities for width-integrals of mixed projection bodies and affine surface area of mixed bodies, together with their inverse forms.

In this paper, we show that the class of $D$-symmetric operators is norm dense in ${\mathcal L(H)}$. It is known that the direct sum of two $D$- symmetric operators are not $D$-symmetric in general. Here we will show that the direct sum of two $D$-symmetric operators is $D$-symmetric if their spectrums do not meet each other. As a consequence, we show that the set $T+K: T$ is $D-$symmetric and $K$ is compact is norm dense. Some open problems are also presented

The object of this paper is to solve the so--called modified entropy equation \[ f\left(x, y, z\right)=f\left(x, y+z, \mathbf{0}\right)+ \mu\left(y+z\right)f\left(\mathbf{0}, \frac{y}{y+z}, \frac{z}{y+z}\right), \] on the positive cone of ${\mathbb R}^{k}$, where $\mu$ is a given multiplicative function on this cone. After that the regular solutions of this equation are determined. Furthermore we investigate its connection between the entropy equation and other equations, as well.

In this paper we give more results about inner radius spectrum of operators on Hilbert spaces with several examples. Also, we established an inequality for inner radius spectrum of a positive operator matrix and its minimum moduli block matrix.

We investigate the following generalized Cauchy functional equation \[ f(\alpha x+\beta y)=\alpha f(x)+\beta f( y) \] where $\alpha,\beta\in \Bbb{R}\setminus\{0\},$ and use a fixed point method to prove its generalized Hyers-Ulam-Rassias stability in Banach modules over a $C^*$-algebra.

This paper provides some new bounds for $1-$norms of positive triangular matrices with monotonic column entries. The main theorem refines a recent inequality of Vecchio and Mallik in the case of constant diagonal. The results are shown to be in a sense best possible under the given constraints. En route some partial order inequalities are obtained.