a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

Let Bc denote the real-valued functions continuous on the extended real line and vanishing at −∞. Let Br denote the functions that are left continuous, have a right limit at each point and vanish at −∞. Define Ac to be the space of tempered distributions that are the nth distributional derivative of a unique function in Bc. Similarly with A n r from Br. A type of integral is defined on distribu...

In this paper we use the standard terminology and notations of the Riesz spaces theory (see [2]). The Banach lattice of the continuous functions from a compact Hausdorff space into a Banach lattice E is denoted by C(K,E). If E = R then we write C(K) instead of C(K,E). 1 stands for the unit function in C(K). One version of the Banach–Stone theorem states that: Theorem 1. Let X and Y be compact H...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

We create a new family of Banach spaces, the James–Schreier spaces, by amalgamating two important classical Banach spaces: James’ quasi-reflexive Banach space on the one hand and Schreier’s Banach space giving a counterexample to the Banach–Saks property on the other. We then investigate the properties of these James–Schreier spaces, paying particular attention to how key properties of their ‘a...

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

We show that if a separable Banach space Z contains isometric copies of every strictly convex separable Banach space, then Z actually contains an isometric copy of every separable Banach space. We prove that if Y is any separable Banach space of dimension at least 2, then the collection of separable Banach spaces which contain an isometric copy of Y is analytic non Borel.