the goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--archimedean spacesand also in $p$--banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

We investigate various kinds of bases in infinite dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain c...

A central question in Banach space theory has been to identify the class of Banach spaces that contain almost isometric copies of the classical sequence spaces `p and c0. Banach space theory entered a new era in the mid 1970’s, when B. Tsirelson [34] constructed the first space not containing isomorphic copies any of the classical sequence spaces. Tsirelson’s space has been called “the first tr...

We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modul...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (ek) is said to be subsequentially minimal if for every normalized block basis (xk) of (ek), there is a further block (yk) of (xk) such that (yk) is equivalent to a subsequence of (ek). Sufficient conditions are given for a partly modified mixed Tsirelson space to be s...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

A sequence {vj} is said to be Cauchy if for each > 0, there exists a natural number N such that ‖vj−vk‖ < for all j, k ≥ N . Every convergent sequence is Cauchy, but there are many examples of normed linear spaces V for which there exists non-convergent Cauchy sequences. One such example is the set of rational numbers Q. The sequence (1.4, 1.41, 1.414, . . . ) converges to √ 2 which is not a ra...

In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (ek) is said to be subsequentially minimal if for every normalized block basis (xk) of (ek), there is a further block basis (yk) of (xk) such that (yk) is equivalent to a subsequence of (ek). Sufficient conditions are given for a partly modified mixed Tsirelson space t...