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1

On the analytic α-Lipschitz vector-valued operators

Shokri Abbasali

Journal of Mathematics and Applications

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2022

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Vol. 45

181--190

EN

Let (X, d) be a non-empty compact metric space in C, (B, ∥ . ∥) be a commutative unital Banach algebra over the scalar field F(= R or C) and α ∈ R with 0 < α ≤ 1. In this work, first we define the analytic α-Lipschitz B-valued operators on X and denote the Banach algebra of all these operators by Lipα A(X, B). When B = F, we write Lipα A(X) instead of Lipα A(X, B). Then we study some interesting results about Lipα A(X, B), including the relationship between Lipα A(X, B) with Lipα A(X) and B, and also characterize the characters on Lipα A(X, B).

2

Existence results for nonlinear coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type

Nabil Tamer

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

236--248

EN

The combined systems of integral equations have become of great importance in various fields of sciences such as electromagnetic and nuclear physics. New classes of the merged type of Urysohn Volterra-Chandrasekhar quadratic integral equations are proposed in this paper. This proposed system involves fractional Urysohn Volterra kernels and also Chandrasekhar kernels. The solvability of a coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type is studied. To realize the existence of a solution of those mixed systems, we use the Perov’s fixed point combined with the Leray-Schauder fixed point approach in generalized Banach algebra spaces.

3

On some fixed point theorems for expansive mappings in dislocated cone metric spaces with Banach algebras

Auwalu Abba, Hinçal Evren, Mishra Lakshmi Narayan

Journal of Mathematics and Applications

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2019

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Vol. 42

21--33

EN

In this paper, we introduced the notion of generalized expansive mappings in dislocated cone metric spaces with Banach algebras. Furthermore, we prove some ﬁxed point theorems for generalized expansive mappings in dislocated cone metric spaces with Banach algebras without the assumption of normality of cones. Moreover, we give an example to elucidate our result. Our results are signiﬁcant extension and generalizations of many recent results in the literature.

4

Derivations into annihilators of the ideals of Banach algebras

Teymouri Akram, Bodaghi Abasalt, Bagha Davood Ebrahimi

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

20--28

EN

In this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A. We compare these notions with Ј-weak amenability and ideal amenability, where Ј is a closed two-sided ideal in A. We also study the hereditary properties of quotient ideal amenability for Banach algebras. Some examples show that the concepts of A/Ј-weak amenability and of Ј-weak amenabilitydo not coincide for Banach algebras in general.

5

Measures of noncompactness in a Banach algebra and their applications

Dudek S.

Journal of Mathematics and Applications

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2017

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Vol. 40

69--84

EN

In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.

6

Maximal ideal space of certain α-Lipschitz operator algebras

Shokri A. A., Shokri A.

Journal of Mathematics and Applications

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2012

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Vol. 35

83--89

EN

In a recent paper by A. Ebadian and A.A. Shokri [1], a α-Lipschitz operator from a compact metric space X into a unital bounded commutative Banach algebra B is defined. Let (X,d) be a nonempty compact metric space, 0<α≤1 and (B, || . ||) be a unital bounded commutative Banach algebra. Let Lipα(X,B) be the algebra of all bounded continuous operators ƒ: X → B such that [formula/wzor]. In this work, we characterize the maximal ideal space of Lipα(X,B).

7

On composition operator in the algebra of functions of two variables with bounded total Φ-variation in Schramm sense

Ereu T., Merentes N., Rzepka B., Sanchez J. L.

Journal of Mathematics and Applications

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2010

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Vol. 33

35-50

EN

In this paper we consider the so called composition operator being a self-mapping of the Banach algebra of the function of two variables with bounded total Φ-variation in the Schramm sense. The main result of the paper characterizes the composition operator mentioned above which has a generating function being Lipschitzian with respect to the second variable. The basic tool used in our considerations is the concept of the left-left regularization.

8

Functions of two variables with bounded φ-variation in the sense of Riesz

Aziz W., Leiva H., Merentes N., Sánchez J. L.

Journal of Mathematics and Applications

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2010

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Vol. 32

5-23

EN

In this paper we introduce the concept of bounded φ- variation function, in the sense of Riesz, dened in a rectangle [wzór]. We prove that the linear space [wzór] generated by the class [wzór] of all φ-bounded variation functions is a Banach algebra. Moreover, we give necessary and sucient conditions for the Nemytskii operator acting in the space [wzór] to be globally Lipschitz.

9

Spectra of the operator of the first difference in salpha, s)/alpha and lp (alpha) (1

Fares A., Malafosse B.

Demonstratio Mathematica

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2008

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Vol. 41, nr 3

661-676

EN

In this paper we deal with the spectrum of the operator of the first difference A considered as an operator from E to itself where E is one of the sets [...].We apply these results to characterize matrix transformations mapping in E [...] or N. This paper generalizes some results given in [8] and [3].

10

Pairs of derivations on rings and Banach algebras

Wei F., Xiao Z.

Demonstratio Mathematica

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2008

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Vol. 41, nr 2

297-308

EN

We give a generalization of Vukman's theorem concerning a pair of derivations on rings. Then applying this purely algebraic result we obtain several range inclusion results of pair of derivations on Banach algebras.

11

An identity with derivations on rings and Banach algebras

Fosner A., Fosner M., Vukman J.

Demonstratio Mathematica

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2008

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Vol. 41, nr 3

525-530

12

A note Gateaux differentials of hermitian elements in Banach algebras

Herzog G., Schmoeger C.

Demonstratio Mathematica

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2008

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Vol. 41, nr 4

909-913

EN

Let A be a complex unital Banach algebra with unit 1. If a is an element of A is hermitian then we show that [...] and we give a proof of an inequality due to J. Nieto.

13

Stability of the equation of ring homomorphisms

Ger R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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Vol. 12

29-35

EN

Let R be a unitary ring and (A,║‧║) stand for a Banach algebra with a unit. In connection with some stability results of R. Badora [1] and D.G. Bourgin [2] concerning the system of two Cauchy functional equations [formula] for mappings f : R→ A, we deal with Hyers-Ulam stability problem for a single equation f(x + y) + f(xy) = f(x) + f(y) + f(x)f(y). The basic question whether or not equation (**) is equivalent to the system (*) has widely been examined by J. Dhombres [3] and the present author in [4] and [5].

14

On some equations related to derivations in rings and Banach algebras

Vukman J., Kosi-Ulbl I.

Demonstratio Mathematica

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2006

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Vol. 39, nr 1

61-66

EN

The main purpose of this paper is to investigate additive mapping D : R -> R, where R is a (m + n +1)! and \m2 + n2 - m - n - 4mn\ -torsion free semiprime ring with the identity element, satisfying the relation 2D(xm+n+l) = (m+-n+1)(xmD(x)xn +-xnD(x)xm), for all is an element of R and some integers m > 1, n > 1, m2 + n2 - m - n - 4mn /=0.

15

Banach algebra homomorphisms via orthogonal projections

Herzog G., Schmoeger C.

Demonstratio Mathematica

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2006

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Vol. 39, nr 1

137-148

EN

Let A be a unital complex Banach algebra with unit e, and p1,... ,pn a collection of orthogonal projections with sum e. The aim of this note is to investigate the close connections of properties of a is an element of A and of (piapj) ia an element of Mn(A), where Mn(A) denotes the matrix algebra of all n x n matrices with entries in A.

16

Sublinear Functionals and Weak - compatness

Ger R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2005

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Vol. 10

67--76

EN

Let X be a real locally convex linear topological space. A functional f : X → lR is called sublinear provided that f is subadditive and f(nx) = nf(x),x ∈ X,n ∈ IN. We establish a one-to-one correspondence between the collectron of all sublinear functional satisfying some mild regularity conditions and the family of all nonempty convex and weakly"- compact subsets of the dual space X*.

17

The strict topology on topological algebras

Khan L., Mohammad N., Thaheem A.

Demonstratio Mathematica

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2005

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Vol. 38, nr 4

883--894

EN

In this paper, we define strict, uniform and compact-open topologies on a topological algebra and investigate their properties. These results unify and include several results of other authors.

18

Commutativity up to a factor in Banach algebras

Schmoeger C.

Demonstratio Mathematica

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2005

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Vol. 38, nr 4

895--900

EN

In this note we explore commutativity up to a factor ab = alfa ba for Hermitian or normal elements of a complex Banach algebra. Our results generalize results obtained for bounded linear operators on Hilbert spaces.

19

Spectral properties of generalized inverses

Schmoeger Ch.

Demonstratio Mathematica

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2004

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Vol. 37, nr 1

137--148

EN

Let A denote a unital complex Banach algebra. An element a € A is said to be relatively regular if aba = a for some b 6 A. Then b will be called a generalized inverse of a. In this note we study spectral properties of generalized inverses of a.

20

Functionals on Banach algebras with scattered spectra

Mustafayev H. S.

Bulletin of the Polish Academy of Sciences. Mathematics

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2004

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Vol. 52, nr 4

395-403

EN

Let A be a complex, commutative Banach algebra and let M[A] be the structure space of A. Assume that there exists a continuous homomorphism h : L^1(G) --> A with dense range, where L^1(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space M[A] is scattered (i.e., M[A] has no nonempty perfect subset). (b) Weakly almost periodic functionals on A with compact scattered spectra are almost periodic. (c) If M[A] is scattered, then the algebra A is Arens regular if and only if A* = span M[A].