The bounded approximate version of $varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded ap...

In this paper, we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the so-called approximate multiplier rule. In establishing the link between the approximate and the exact multiplier rule we first derive an approximate multiplier rule for a very general class of optimization problems using the approximate sum rule and the chain rule. We als...

We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R. J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtain...

Let A be a Banach algebra with a bounded left approximate identity. The Cohen Factorization Theorem is used to prove several results concerning the representation theory of A.

In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We also obtain some results for perturbations of approximate duals.

Approximate multipliers are widely being advocated for energy-efficient computing in applications that exhibit an inherent tolerance to inaccuracy. However, the inclusion of accuracy as a key design parameter, besides the performance, area and power, makes the identification of the most suitable approximate multiplier quite challenging. In this paper, we identify three major decision making fac...

A Parallel multiplier using approximate compressors are proposed in this paper. The two new approximate 4-2 compressors are proposes that the simplified compressors have better power consumption than the optimized 4-2 compressor existing designs. These approximate compressors are then used in the restoration module of a Parallel multiplier. Four different schemes for utilizing the proposed appr...

The Posit™ Number System was introduced in 2017 as a replacement for floating-point numbers. Since then, the community has explored its application several areas, such deep learning, and produced some unit designs which are still far from being competitive with their counterparts. This article proposes Posit Logarithm-Approximate Multiplication (PLAM) scheme to significantly reduce complexity o...

We investigate the higher-dimensional amenability of tensor products A ⊗̂ B of Banach algebras A and B. We prove that the weak bidimension dbw of the tensor product A⊗̂B of Banach algebras A and B with bounded approximate identities satisfies dbwA ⊗̂ B = dbwA+ dbwB. We show that it cannot be extended to arbitrary Banach algebras. For example, for a biflat Banach algebra A which has a left or right...