In this paper, we give characterizations of retro Banach frames in Banach spaces. The notion of almost exact retro Banach frame is defined and a characterization of retro Banach frame has been given. Also results exhibiting relationship between frames, almost exact retro Banach frames and Riesz bases has been proved. Finally, we give some perturbation results of retro Banach frames and an almos...

In this paper, we analyze Levitan and Bebutov metrical approximations of functions $F :\Lambda \times X \rightarrow Y$ by trigonometric polynomials $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n}$, $X$ $Y$ are complex Banach spaces, $\rho$ is a general binary relation on $Y$. We also various classes multidimensional almost periodic in metric uniformly rec...

It is proved that there exist complemented subspaces of countable topo-logical products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces The problem of description of complemented subspaces of a given locally convex space is one of the general problems of structure theory of locally convex spaces. In ...

Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A satisfactory answer, in the context of reflexive Banach spaces, has been obtained some years ago. Recently, a partial result on non-reflexive Banach spaces w...

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...

A projectional skeleton in a Banach space is a σ-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko spaces (i.e. Banach spaces with a countably norming Markushevich basis). We show that every space with a projectional skeleton has a projectional resolution of the ...

In this paper, we discuss the existence and uniqueness of xed points for Banach and Kannancontractions dened on modular spaces endowed with a graph. We do not impose the Δ2-conditionor the Fatou property on the modular spaces to give generalizations of some recent results. Thegiven results play as a modular version of metric xed point results.

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

The first part of the paper is devoted to metric characterizations of Banach spaces with no cotype and no type > 1 in terms of graphs with uniformly bounded degrees. In the second part we prove that Banach spaces containing bilipschitz images of the infinite diamond do not have the RadonNikodým property and give a new proof of the Cheeger-Kleiner result on Banach spaces containing bilipschitz i...