for all f ∈ H. In general Banach spaces one cannot use just the equivalence of norms similar to (1.1). The above construction breaks down because, in this case, the analysis operator ends up being bounded below and not necessarily left invertible. As a result a “frame decomposition” remains possible but “frame reconstruction” no longer makes sense. In case of localizaed frames, however, this ob...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

The Leray–Schauder degree is defined for mappings of the form I−C, where C is a compact mapping from the closure of an open bounded subset of a Banach space X into X. Since the fifties, a lot of work has been devoted in extending this theory to the same type of mappings on some nonlinear spaces, and in extending the class of mappings in the frame of Banach spaces or manifolds. New applications ...

In this article, we consider an implicit iterative scheme for two asymptotically quasi-I-nonexpansive mappingsS1, S2 and two asymptotically quasi-nonexpansive mapping I1, I2 in Banach space. We obtain convergence results for considered iteration to common fixed point of two asymptotically quasi-I-nonexpansive mappings, asymptotically quasi-nonexpansive mapping and equilibrium problem in frame w...

In this paper we study existence, uniqueness and other properties of solutions Volterra type ABC fractional integral equations. We have used Banach fixed point theorem with Bielecki norm Gronwall inequality in the frame for proving our results.

In principle it is well known that for sufficiently nice wavelet functions the regularity of the wavelet transform allows to recover any L-function from its samples over any sufficiently dense, irregular sampling set. Equivalently, the (irregular) set of affine transforms of the given wavelet function forms a frame for L(R). In the present paper a systematic treatment of sufficient conditions f...

The theory of localized frames is refined to include quasi-Banach spaces and spaces with multiple generators. Applications are given to non-linear approximation with frames and to the convergence of the iterative frame algorithm in finer norms, and to the characterization of Besov spaces with wavelet frames.

In this paper we study the action of a double infinite matrix A on f ∈ H ν (weighted Banach space, 1 ≤ p ≤ ∞) and on its wavelet coefficients. Also, we find the frame condition for A−transform of f ∈ H ν whose wavelet series expansion is known.

This article deals with a nonlinear implicit fractional differential equation nonlocal integral-multipoint boundary conditions in the frame of Hilfer derivative. The existence and uniqueness results are obtained by using fixed point theorems Krasnoselskii Banach. Further, to demonstrate effectiveness main results, suitable examples granted.