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Mohammad Sal Moslehian

Publications and source records attributed to Mohammad Sal Moslehian.

98 records · Page 6Linked to original sources
arXiv2005

More on Reverse Triangle Inequality in Inner Product Spaces

Refining some results of S. S. Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if $a$ is a unit vector in a real or complex inner product space $(H;< .,.>)$, $r, s>0, p\in(0,s], D=\{x\in H,\|rx-sa\|\leq p\}, x_1, x_2\in D-\{0\}$ and $ α_{r,s}=\min\{\frac{r^2\|x_k\|^2-p^2+s^2}{2rs\|x_k\|}: 1\leq k\leq 2 \}$, then $$\frac{\|x_1\|\|x_2\|-Re< x_1,x_2>}{(\|x_1\|+\|x_2\|)^2}\leq α_{r,s}.$$

math.FA↗
arXiv2005

On the Cauchy--Rassias Inequality and Linear n-Inner Product Preserving Mappings

We prove the Cauchy-Rassias stability of linear n-inner product preserving mappings in $n$-inner product Banach spaces. We apply the Cauchy-Rassias inequality that plays an influencial role in the subject of functional equations. The inequality was introduced for the first time by Th.M.Rassias in his paper entitled: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math.Soc. 72(1978), 297-300.

math.FA↗
arXiv2005

A Survey on the Complemented Subspace Problem

The complemented subspace problem asks, in general, which closed subspaces $M$ of a Banach space $X$ are complemented; i.e. there exists a closed subspace $N$ of $X$ such that $X=M\oplus N$? This problem is in the heart of the theory of Banach spaces and plays a key role in the development of the Banach space theory. Our aim is to investigate some results on complemented subspaces, to give a history of the subject, and to present some open problems.

math.FA↗
arXiv2005

On (Co)Homology of Triangular Banach Algebras

Suppose that A and B are unital Banach algebras with units 1_A and 1_B, respectively, M is a unital Banach A-B-bimodule, T=Tri(A,M,B) is the triangular Banach algebra, X is a unital T-bimodule, X_{AA}=1_AX1_A, X_{BB}=1_BX1_B, X_{AB}=1_AX1_B and X_{BA}=1_BX1_A. Applying two nice long exact sequences related to A, B, T, X, X_{AA}, X_{BB}, X_{AB} and X_{BA} we establish some results on (co)homology of triangular Banach algebras.

math.FA↗
arXiv2005

Approximate $(σ-τ)$-Contractibility

In this paper, the generalized Hyers--Ulam--Rassias stability of $(σ-τ)$-derivations on normed algebras into Banach bimodules is established. We introduce the notion of approximate $(σ-τ)$-contractibility and prove that a Banach algebra is $(σ-τ)$-contractible if and only if it is approximately $(σ-τ)$-Contractible.

math.FA↗
arXiv2004

On the stability of the orthogonal Pexiderized Cauchy equation

We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers--Ulam stability of the orthogonal Cauchy functional equation of Pexider type $f_1(x+y)=f_2(x)+f_3(y)$, $x\perp y$ in which $\perp$ is the orthogonality in the sense of Ratz.

math.FA↗