we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

The major goal of this research paper is to investigate the existence and uniqueness an implicit fractional pantograph equation in frame Hilfer-Katugampola operator on finite interval $[a,b]$ with mixed nonlocal conditions. Our analysis solutions depends some fixed point theorems such as Banach Krasnoselskii. Moreover, we discuss dependence conditions by means $\delta $-approximated solution. A...

Abstract In this work, we establish some necessary results about existence theory to a class of boundary value problems (BVPs) hybrid fractional differential equations (HFDEs) in the frame Atangana–Baleanu–Caputo ( ABC ) derivative. Making use Krasnoselskii and Banach theorems, obtain required conditions. Some appropriate Hyers–Ulam (H–U) stability corresponding considered problem are also esta...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

Abstract This study is aimed to investigate the sufficient conditions of existence unique solutions and Ulam–Hyers–Mittag-Leffler (UHML) stability for a tripled system weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in frame Chebyshev Bielecki norms with time delay. The acquired results are obtained using Banach fixed point theorems Pic...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

let $a$ be a banach algebra and $x$ be a banach $a$-bimodule. then ${mathcal{s}}=a oplus x$, the $l^1$-direct sum of $a$ and $x$ becomes a module extension banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ in this paper, we investigate biflatness and biprojectivity for these banach algebras. we also discuss on automatic continuity of derivations on ${mathcal{s...

motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...