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In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some additive results on gp-Hirano invertibility in Banach algebras. By applying our results, some new results for operator matrices are obtained. This extends the main results of [H. Zou, T. Li and Y. Wei, arXiv:2302.06080v1]. [ABSTRACT FROM AUTHOR]

In this paper, we discuss some extensions of the Maligranda–Orlicz lemma. It deals with the problem of constructing a norm in a subspace of the space of bounded functions, for which it becomes a normed algebra so that the norm introduced is equivalent to the initial norm of the subspace. This is done by satisfying some inequality between these norms. We show in this paper how this inequality is relevant to the study of operator equations in Banach algebras. In fact, we study how to equip a subspace of the space of bounded functions with a norm equivalent to a given one so that it is a normed algebra. We give a general condition for the construction of such norms, which allows us to easily check whether a space with a given norm is an algebra with a pointwise product and the consequences of such a choice for measures of noncompactness in such spaces. We also study quasi-normed spaces. We introduce a general property of measures of noncompactness that allows the study of quadratic operator equations, prove a fixed-point theorem suitable for such problems, and complete the whole with examples and applications. [ABSTRACT FROM AUTHOR]

In this paper, we study a connection between the operator Riccati equation S′(x) = KS(x) + S(x)K - 2S(x)KS(x), x ∈ R, and the set of reflectionless Schr¨odinger operators with operator-valued potentials. Here K ∈ B(H), K > 0 and S: R → B(H), where B(H) is the Banach algebra of all linear continuous operators acting in a separable Hilbert space H. Let S+(K) be the set of all solutions S of the Riccati equation satisfying the conditions 0 < S(0) < I and S′(0) ≥ 0, with I being the identity operator in H. We show that every solution S ∈ S+(K) generates a reflectionless Schr¨odinger operator with some potential q that is an analytic function in the strip... [ABSTRACT FROM AUTHOR]

In this paper, using fixed point method, we investigate the stability and also the superstability of cubic bi-derivations on Banach algebras. [ABSTRACT FROM AUTHOR]

In this paper, we present a technique that improves the applicability of the result obtained by Cordero et al. in 2024 for solving nonlinear equations. Cordero et al. assumed the involved operator to be differentiable at least five times to extend a two-step p-order method to order p + 3 . We obtained the convergence order of Cordero et al.'s method by assuming only up to the third-order derivative of the operator. Our analysis is in a more general commutative Banach algebra setting and provides a radius of the convergence ball. Finally, we validate our theoretical findings with several numerical examples. Also, the concept of basin of attraction is discussed with examples. [ABSTRACT FROM AUTHOR]

Invertible members of some of the most famous multiplicative quasilinear spaces are exactly equal to invertible elements of the linear subspace of such spaces. But with the old definition of invertible elements, we do not get anything extra. So, in the present paper, we develop the introductory algebra and introduce an extended model of invertible elements. This new concept plays a fundamental role in the definition of the generalized spectrum model. These new objects are constructed in such a way that can provide acceptable results. For example, we will be able to generalize the well-known theorem “Spectral mapping property for polynomials” with these new notions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and thoroughly examine new generalized  ψ -conformable fractional integral and derivative operators associated with the auxiliary function  ψ (t) . We rigorously analyze and confirm the essential properties of these operators, including their semigroup behavior, linearity, boundedness, and specific symmetry characteristics, particularly their invariance under time reversal. These operators not only encompass the well-established Riemann–Liouville and Hadamard operators but also extend their applicability. Our primary focus is on addressing complex fractional boundary value problems, specifically second-order nonlinear implicit  ψ -conformable fractional integro-differential equations with nonlocal fractional integral boundary conditions within Banach algebra. We assess the effectiveness of these operators in solving such problems and investigate the existence, uniqueness, and Ulam–Hyers stability of their solutions. A numerical example is presented to demonstrate the theoretical advancements and practical implications of our approach. Through this work, we aim to contribute to the development of fractional calculus methodologies and their applications. [ABSTRACT FROM AUTHOR]

In 1989, Bakhtin proved a version of the Banach contraction principle in the context of b-metric spaces. More precisely, let (X, d; s) be a complete b-metric space with parameter s ⩾ 1 and let T a contractive map on X, that is a self-map T of X satisfying d(Tx, Ty) ⩽ λd(x, y), ∀x, y ∈ X, (Bλ) with some λ ∈ [0, 1). Bakhtin proved that if λ ∈ [0, 1 s), then T has a unique fixed point. In the two last decades many research papers were produced by many authors in the setting of b-metric spaces. In 2021, the author published a note on the Banach contraction principle in b-metric spaces in Divilgaciones Mat'ematicas dealing with some complements to Bakhtin results. The aim of this paper is to provide other complements. In particular, we discuss the remaining case where λ ∈ [1 s, 1). We give an evaluation of the order of convergence for the iterative Picard process and a posteriori error estimate for this process and we estimate the diameter of the T-orbits. We investigate well-posedness of the fixed problem of a map T satisfying Bλ when X is Torbitally complete and we establish two shadowing properties for these maps without requiring completeness of X. [ABSTRACT FROM AUTHOR]

In this paper we make an attempt to prove common fixed point theorem for two and three mappings in Banach algebra by using measure of non-compactness. In the second section of the paper we prove the common fixed point theorem for two continuous linear operators on Banach algebra and also an effort is made to prove common fixed point theorem for three continuous commuting operators in Banach algebra. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce a new definition of JA‐module Arens regularity, which extends former standard definition. Then a new module structure on the semigroup algebra l1S as l1ES‐module with nontrivial right and left module actions is constructed. Using this construction, it is also proved that l1S is a Jl1S‐module Arens regular if and only if S/≈ is finite. [ABSTRACT FROM AUTHOR]

This paper considers a coupled hybrid thermostat system driven by the Ã-Caputo fractional derivative in a Banach algebra. We employ a version of Darbo’s fixed-point theorem combined with the measure of noncompactness (MNC) technique to establish certain existence results. Additionally, an example is provided to illustrate our findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra A with respect to its w∗-closed ideal I, say I-Connes biprojectivity. Some Lipschitz algebras Lipα(X) and some matrix algebras are studied under this new notion. Also, with some mild assumptions, the relation between IConnes biprojectivity and left ϕ-contractibility is given, where ϕ is a ω∗-continuous multiplicative linear functional on A. As an application, we characterize Connes biprojectivity of some Lipschitz algebras. [ABSTRACT FROM AUTHOR]

Collage Theorem provides a bound for the distance between an element of a given space and a fixed point of a self-map on that space, in terms of the distance between the point and its image. We give in this paper some results of Collage type for Reich mutual contractions in b-metric and strong b-metric spaces. We give upper and lower bounds for this distance, in terms of the constants of the inequality involved in the definition of the contractivity. Reich maps contain the classical Banach contractions as particular cases, as well as the maps of Kannan type, and the results obtained are very general. The middle part of the article is devoted to the invertibility of linear operators. In particular we provide criteria for invertibility of operators acting on quasi-normed spaces. Our aim is the extension of the Casazza-Christensen type conditions for the existence of inverse of a linear map defined on a quasi-Banach space, using different procedures. The results involve either a single map or two operators. The latter case provides a link between the properties of both mappings. The last part of the article is devoted to study the construction of fractal curves in Bochner spaces, initiated by the first author in a previous paper. The objective is the definition of fractal curves valued on Banach spaces and Banach algebras. We provide further results on the fractal convolution of operators, defined in the same reference, considering in this case the nonlinear operators. We prove that some properties of the initial maps are inherited by their convolutions, if some conditions on the elements of the associated iterated function system are satisfied. In the last section of the paper we use the invertibility criteria given before in order to obtain perturbed fractal spanning systems for quasi-normed Bochner spaces composed of Banach-valued integrable maps. These results can be applied to Lebesgue spaces of real valued functions as a particular case. [ABSTRACT FROM AUTHOR]

Let A be a Banach algebra. An element a ϵ A has generalized Drazin inverse if there exists b ϵ A such that b = bab, ab = ba, a - a²b ϵ Aqnil. New additive results for the generalized Drazin inverse of an operator over a Banach space are presented. we extend the main results of a paper of Shakoor, Yang and Ali from 2013 and of Wang, Huang and Chen from 2017. Appling these results to 2 x 2 operator matrices we also generalize results of a paper of Deng, Cvetković-Ilić and Wei from 2010. [ABSTRACT FROM AUTHOR]

The purpose of this paper was to introduce several b-generalized contractive mappings in the framework of cone b-metric spaces over Banach algebras. The obtained contractions generalized and extended the counterparts in metric spaces, cone metric spaces, and b-metric spaces. Moreover, via weakening the completeness of the spaces, we gave some fixed point theorems for asymptotically regular mappings without considering the orbital continuity and k-continuity of the mappings. Those who need a specification is our results do not rely on the continuity of b-metric and the normality of cones. In addition, some nontrivial examples were presented to illustrate the superiority of our fixed point theorems. [ABSTRACT FROM AUTHOR]

Let n ≥ 2 be a fixed integer and A be a C ∗ -algebra. A permuting n-linear map G : A n → A is known to be symmetric generalized n-derivation if there exists a symmetric n-derivation D : A n → A such that G ς 1 , ς 2 , ... , ς i ς i ′ , ... , ς n = G ς 1 , ς 2 , ... , ς i , ... , ς n ς i ′ + ς i D (ς 1 , ς 2 , ... , ς i ′ , ... , ς n) holds ∀ ς i , ς i ′ ∈ A . In this paper, we investigate the structure of C ∗ -algebras involving generalized linear n-derivations. Moreover, we describe the forms of traces of linear n-derivations satisfying certain functional identity. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the existence and uniqueness of continuous solutions of the following iterative functional differential equation ... By using of Boyd-Wong's fixed point theorem and under suitable conditions, we establish the existence and uniqueness of a continuous solution. [ABSTRACT FROM AUTHOR]

Let X be a nonempty set, A be a commutative Banach algebra, and 1 ≤ p < ∞. In this paper, we present a concise proof for the result concerning the BSE (Banach space extension) property of ℓ p X , A . Specifically, we establish that ℓ p X , A possesses the BSE property if and only if X is finite and A is BSE. Additionally, we investigate the BSE module property on Banach ℓ p X , A -modules and demonstrate that a Banach space ℓ p X , Y serves as a BSE Banach ℓ p X , A -module if and only if X is finite and Y represents a BSE Banach A -module. [ABSTRACT FROM AUTHOR]

In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the p -power-radical functional equation related to sine function equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = f (x) f (y) from an approximation of the p -power-radical functional equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = g (x) h (y) , where p is a positive odd integer, and f , g and h are complex valued functions on R . Furthermore, the obtained results are extended to Banach algebras. In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the p -power-radical functional equation related to sine function equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = f (x) f (y) from an approximation of the p -power-radical functional equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = g (x) h (y) , where p is a positive odd integer, and f , g and h are complex valued functions on R . Furthermore, the obtained results are extended to Banach algebras. [ABSTRACT FROM AUTHOR]

Let A be a Banach algebra and n > 1 , a fixed integer. The main objective of this paper is to talk about the commutativity of Banach algebras via its projections. Precisely, we prove that if A is a prime Banach algebra admitting a continuous projection P with image in Z (A) such that P (a n) = a n for all a ∈ G , the nonvoid open subset of A , then A is commutative and P is the identity mapping on A . Apart from proving some other results, as an application we prove that, a normed algebra is commutative iff the interior of its center is non-empty. Furthermore, we provide some examples to show that the assumed restrictions cannot be relaxed. Finally, we conclude our paper with a direction for further research. [ABSTRACT FROM AUTHOR]

Let A be an algebra with a right identity. In this paper, we study (p, q)−centralizers of A and show that every (p, q)−centralizer of A is a two-sided centralizer. In the case where, A is normed algebra, we also prove that (p, q)−centralizers of A are bounded. Then, we apply the results for some group algebras and verify that L 1 (G) has a nonzero weakly compact (p, q)−centralizer if and only if G is compact and the center of L 1 (G) is non-zero. Finally, we investigate (p, q)−Jordan centralizers of A and determine them. [ABSTRACT FROM AUTHOR]

Let G be a locally compact hypergroup and K be a compact subhypergroup of G such that (G, K) is a Gelfand pair. For a Banach algebra A, L¹ (G, A) denotes the A-valued L¹-space on G. In this paper, we extend the generalized Wendel theorem to L¹ (G,A), the subspace of K-invariant functons of L¹ (G, A), when A is a Banach algebra with identity. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [ 0 ,   1 ] , but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric space which generalizes, extends and unifies the notion of classical fuzzy metric space and complex-valued fuzzy metric space and permits us to consider the fuzzy sets and metrics in a larger domain. Some topological properties of such spaces are discussed and some fixed point results in this new setting are proved. Multifarious examples are presented which clarify and justify our claims and results. [ABSTRACT FROM AUTHOR]

In this paper, we solve the system of functional equations { f (x + y) + g (y − x) = 2 f (x) , g (x + y) − f (y − x) = 2 g (y) and we investigate the stability of g-derivations in Banach algebras. [ABSTRACT FROM AUTHOR]

In this paper, the existence of the solutions of a class of weakly singular integral equations in Banach algebra is investigated. The basic tool used in investigations is the technique of the measure of non-compactness and Petryshyn's fixed point theorem. Also, for the applicability of the obtained results, some examples are given. [ABSTRACT FROM AUTHOR]

Introduction The notion of amenability for Banach algebras was first introduced and initiated by Johnson [3]. Afterwards, Gronbaek [2] studied the concept of cyclic amenability and it‘s hereditary properties of Banach algebras. Many Authors study and investigate the several notions of σ-amenability, for more details refer to [1], [5], [6], [8] and [9]. In the throughout of this paper we assume that A is a Banach algebra, I is a closed two-sided ideal in A, σ is a continuous homomorphism on A and X is an A-bimodule Banach. The linear map D: A→X is called derivation if D(ab) = D(a)∙b + a∙D(b) for all a,bϵA. Moreover, the linear mapping D: A → X is called a σ-derivation if D(ab) = D(a)∙σ(b) + σ(a)∙D(b) for each a,bϵA. A linear map D : A → X is called σ-inner derivation if there exists x1∈X such that D = adσx1, where adσx1(a) = σ(a).x1-x1.σ(a), for all a∈A. The Banach algebra A is called σ-amenable if every σ-derivation D : A → X∗ is σ-inner. This notion was first introduced and studied by Moslehian and Motlagh [9]. Recall that the derivation D:A→A∗ is cyclic if +=0, (a,bϵA). A is cyclic amenable if every cyclic derivation D:A→A∗ is inner. So, by using these notion we introduced the new notions σ-cyclic derivation and σ-cyclic amenability for Banach algebras. We say that the σ-derivation D : A → A∗ is σ-cyclic if ⟨D(a), σ(b)⟩ + ⟨D(b), σ(a)⟩ = 0, (a,bϵA). Also, the Banach algebra A is σ-cyclic amenable if every σ-cyclic derivation D:A→A∗ is σ-inner. The closed two-sided ideal I in A has the trace extension property if for each λϵI∗ with a∙λ=λ∙a (aϵA), there exists ΛϵA∗ such that Λ|I = λ and Λ∙a=a∙Λ, for all aϵA. Every homomorphism σ on A can be extended to a homomorphism σ̂: A/I → A/I suth that for aϵA defined by σ̂(a+I)=σ(a)+I. Next, we present the results obtained in this paper. We showed that let A/I be σ̂-cyclic amenable. Then I has the trace extension property. Also, Suppose that σ has dense range on A, I has the trace extension property and Ais σ-cyclic. Then A I is σ̂-cyclic amenable. Recall that the Banch algebra A is essential, if A̅̅2 = A. We showed that every σ-cyclic amenable Banach algebra is essential. If σ(I) ⊆ I, we can restrict σ to I and denoted it by σI :I → I. It is clear that σI is continuous homomorphism on I. Thus, if σ(I) ⊆ I, I is σI -cyclic amenable and A/I is σ̂-cyclic amenable, then A is σ-cyclic amenable. For the unitization of Banach algebra A i.e. A#=A ⊕ ℂe, and for every continuous homomorphism σ on A there exists a continuous homomorphism σ# : A# → A# such that defined by σ# (a, λe)=σ(a)+λe, (aϵA, λϵℂ). Therefore, with above notes, A is σ-cyclic amenable if and only if A# be σ# -cyclic amenable. Finally, for two Banach algebras A and B and nonzero multiplicative linear functional θ on B, the Cartesian space A×B with norm and multiplication ||(a,b)||=||a||+||b||, (a,b)(a’,b’)=(aa’+θ(b)a’+θ(b’)a, bb’), is a Banach algebra and denoted by A×𝜃𝐵. If σ and τ are homomorphisms on A and B respectively, then (σ, τ) denoted by <(σ, τ),(a, b)>=(σ(a), τ(b)) is a homomorphism on A×𝜃𝐵 if and only if θ∘τ=θ. By using this we showed that A×𝜃𝐵 is (σ, τ)-cyclic amenable if and only if A is σ-cyclic amenable and B is τ-cyclic amenable. [ABSTRACT FROM AUTHOR]

In this paper, we introduce triple θ-centralizers and weak triple θ-centralizers on an algebra A, where θ: A → A is a triple homomorphism. Some observations concerning triple θ-centralizers, weak triple θ-centralizers and approximate weak triple θ-centralizers are given. [ABSTRACT FROM AUTHOR]

The equivariant coarse Baum--Connes conjecture interpolates between the Baum--Connes conjecture for a discrete group and the coarse Baum--Connes conjecture for a proper metric space. In this paper, we study this conjecture under certain assumptions. More precisely, assume that a countable discrete group Γ acts properly and isometrically on a discrete metric space X with bounded geometry, not necessarily cocompact. We show that if the quotient space X/Γ admits a coarse embedding into Hilbert space and Γ is amenable, and that the Γ-orbits in X are uniformly equivariantly coarsely equivalent to each other, then the equivariant coarse Baum--Connes conjecture holds for (X; Γ). Along the way, we prove a K-theoretic amenability statement for the Γ-space X under the same assumptions as above; namely, the canonical quotient map from the maximal equivariant Roe algebra of X to the reduced equivariant Roe algebra of X induces an isomorphism on K-theory. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the general solution and the Hyers-Ulam stability of the system of biadditive functional equations ... in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of f -biderivations in complex Banach algebras. [ABSTRACT FROM AUTHOR]

The first goal of this paper is to find a representation of the Fock space on C n in terms of the weighted Bergman spaces of the projective spaces CP n − 1 ; i.e., every function in the Fock space can be written as a direct sum of elements in weighted Bergman space on CP n − 1 . Also, we study the C * algebras generated by Toeplitz operators where the symbols are taken from the following two families of functions: Firstly, the symbols depend on the moment map associated with the unit circle, and secondly, the symbols are invariant under the same action. Moreover, we analyze the commutative relations between these algebras, and we apply these results to find new commutative Banach algebras generated by Toeplitz operators on Fock space of C n . [ABSTRACT FROM AUTHOR]

In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on 1 E -complete multiplicative partial cone metric spaces over Banach algebras and formulate some existence and uniqueness results regarding the fixed-point theorems using some integrative conditions. Moreover, we validate the significance our results and exploit them to find the unique solution of a fractional nonlinear differential equation of Caputo type, which complements some previously well-known generalizations found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider rings of multisets consisting of elements of a Banach algebra. We investigate the algebraic and topological structures of such rings and the properties of their homomorphisms. The rings of multisets arise as natural domains of supersymmetric functions. We introduce a complete metrizable topology on a given ring of multisets and extend some known results about structures of the rings to the general case. In addition, we consider supersymmetric polynomials and other supersymmetric functions related to these rings. This paper contains a number of examples and some discussions. [ABSTRACT FROM AUTHOR]

This paper investigates the existence and uniqueness of implicit solutions in a coupled symmetry system of hybrid fractional order differential equations, along with hybrid integral boundary conditions in Banach Algebras. The methodology centers on a hybrid fixed-point theorem that involves mixed Lipschitz and Carathéodory conditions, serving to establish the existence of solutions. Moreover, it derives sufficient conditions for solution uniqueness and establishes the Hyers–Ulam types of solution stability. This study contributes valuable insights into complex hybrid fractional order systems and their practical implications. [ABSTRACT FROM AUTHOR]

In this paper, we study the generalized Fourier-Feynman transform (GFFT) for functions on the general Wiener space Ca,b[0,T]. We establish an explicit evaluation formula for the analytic GFFT of bounded cylinder functions on Ca,b[0, T]. We start by examining certain cylinder functions which belong in a Banach algebra of bounded functions on Ca,b[0,T]. We then obtain an explicit formula for the analytic GFFT of the bounded cylinder functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type of contractive mappings defined on such spaces. These results extend and generalize several results from metric, graphical metric, and cone metric spaces. Some examples that demonstrate the results proved herein are provided. An application of our results to the existence of solution of a pair of initial value problems is provided. [ABSTRACT FROM AUTHOR]

In this paper, some properties of a generalized translation operator are obtained. A weight dependent convolution product on Beurling spaces is studied. A convolution theorem related to a weight Fourier transform is obtained. Multipliers for the pair (L¹ω(G),Lpω(G)) are introduced. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of soft multiplicative linear functional in soft Banach algebras. Then the notions of soft spectrum and soft spectral radius of an element in soft Banach algebras are introduced. Furthermore we discuss some important characterizations and theorems of them. [ABSTRACT FROM AUTHOR]

Let R be a prime ring and L a non-central Lie ideal of R. The purpose of this paper is to describe generalized derivations of R satisfying some algebraic identities locally on L. More precisely, we consider two generalized derivations F1 and F2 of a prime ring R satisfying one of the following identities: 1. F1(x) ◦ y + x ◦ F2(y) = 0, 2. [F1(x), y] + F2([x, y]) = 0, for all x, y in a non-central Lie ideal L of R. Furthermore, as an application, we study continuous generalized derivations satisfying similar algebraic identities with power values on nonvoid open subsets of a prime Banach algebra A. Our topological approach is based on Baire's category theorem and some properties from functional analysis. [ABSTRACT FROM AUTHOR]

Let A be a Banach algebra over R or C with center Z(A). In this paper, we show that, if a non-injective continuous derivation of A satisfies some local differential identities, then A must be commutative. We give several applications, and we provide examples to show that some hypotheses of our theorems are necessary. [ABSTRACT FROM AUTHOR]

In this paper, by some group action, we introduce a new type of weighted Orlicz spaces Lψw,v(O), where w and v are weights on O and ψ is a Young function. We study conditions under which Lψ w,v(G) is a convolution Banach algebra, where G is a locally compact group. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of soft multiplicative linear functional in soft Banach algebras. Then the notions of soft spectrum and soft spectral radius of an element in soft Banach algebras are introduced. Furthermore we discuss some important characterizations and theorems of them. [ABSTRACT FROM AUTHOR]

Nearly 60 years have passed since Lennart Carleson gave his proof of Corona Theorem for unit disc in the complex plane. It was only recently that M. Kosiek and K. Rudol obtained the first positive result for Corona Theorem in multidimensional case. Using duality methods for uniform algebras the authors proved "abstract" Corona Theorem which allowed to solve Corona Problem for a wide class of regular domains. In this paper we expand Corona Theorem to strictly pseudoconvex domains with smooth boundaries. [ABSTRACT FROM AUTHOR]

Let S be a commutative (not necessary unital) inverse semigroup with the set of idempotents E then ℓ¹(S) is a commutative Banach ℓ¹(E)-module with canonical actions . Recently, it is shown that the triangular Banach algebra T = [ ℓ¹(S) M ℓ¹(S) ] is (n)-weakly ℓ¹(E)-module amenable, provided that M = ℓ¹(S) and S is unital or E satisfies condition Dk for some K ∈ ℕ . In this paper, we show that T is (2n + 1)- weakly ℓ¹(E)-module amenable, without any additional conditions on S and E, if M is a certain quotient space of ℓ¹(S). [ABSTRACT FROM AUTHOR]

In this paper, we study a non-local diffusion problem that involves three different fractional Laplacian operators acting on two domains. Each domain has an associated operator that governs the diffusion on it, and the third operator serves as a coupling mechanism between the two of them. The model proposed is the gradient flow of a non-local energy functional. In the first part of the paper, we provide results about existence of solutions and the conservation of mass. The second part encompasses results about the Lp decay of the solutions. The third part is devoted to study, the asymptotic behavior of the solutions of the problem when the two domains are a ball and its complementary. Exterior fractional Sobolev and Nash inequalities of independent interest are also provided in Appendix A. [ABSTRACT FROM AUTHOR]

In this paper, approximate Noether and Lie symmetries of 2nd order for Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) charged black hole in the Einstein frame are analyzed comprehensively. To explore the approximate Noether symmetries of 2nd order, Noether symmetries of Minkowski spacetime are used which forms a 17 dimensional Lie algebra. It is observed that no new approximate Noether symmetry is obtained at 1st and 2nd order. To examine the 1st and 2nd order approximate Lie symmetries of the GMGHS black hole spacetime, 35 Lie symmetries (exact) of the Minkowski spacetime are used which forms an algebra sl(6, R). It is shown that no new approximate Lie symmetry exists at 1st and 2nd order and only exact 35 symmetries are recouped as trivial approximate Lie symmetries at both orders. Furthermore, no energy rescaling factor is seen in this spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we investigate local Lie derivations of a certain class of generalized matrix algebras and show that, under certain conditions, every local Lie derivation of a generalized matrix algebra is a sum of a derivation and a linear central-valued map vanishing on each commutator. The main result is then applied to full matrix algebras and unital simple algebras with nontrivial idempotents. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear n-term fractional quadratic integral equation. Our investigation is located in the space C(J; R): We prove the existence and uniqueness of the solution for that problem by applying some fixed point theorems. Next, we establish the continuous dependence of the unique solution for that problem on some functions. Finally, we present some particular cases for n-term fractional quadratic integral equation and an example to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of solutions for hybrid fractional differential equations involving Caputo fractional derivative of order 2 < ζ 3. We base our arguments on a generalization of Darbo’s fixed point theorem combined with the approaches related with measures of noncompactness in Banach algebras. To demonstrate the argument, an illustration is provided. [ABSTRACT FROM AUTHOR]

In recent papers, it was shown for the biharmonic Schrödinger equation and 2D Schrödinger equation that Fokas method-based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interior-boundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with Dirichlet/Neumann boundary conditions. [ABSTRACT FROM AUTHOR]