In this paper we study the divergence behavior of linear approximation processes in general Banach spaces. We are interested in the structure of the set of divergence creating functions. The Banach–Steinhaus theory gives some information about this set, however, it cannot be used to answer the question whether this set contains subspaces with linear structure. We give necessary and sufficient c...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

In 1958 this was proved independently by S. Swierczkowski [15] and by P. Erdos and V.T. Sos [12],[13]. It is often called the Steinhaus theorem or Steinhaus Conjecture. A useful way of viewing the result is to think of a circle of unit circumference with points placed around the perimeter at distances 0, 0:, ... , (N 1)0: from an arbitrary origin on the perimeter. Then the distances between adj...

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.

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...