In this paper, we study a new class of generalized inverses in Banach algebras, which is termed extended pseudo Drazin inverse. We derive several characterizations and elementary properties of the extended pseudo Drazin inverse. Moreover, we obtain the generalized versions of Jacobson?s lemma for extended Drazin inverse, extended generalized Drazin inverse and extended pseudo Drazin inverse.

In this research article, we introduce and define strong deferred summability and deferred statistical summability within the framework of neutrosophic-n-normed linear spaces (abbreviated as N-n-NLS), and we thoroughly explore their properties. Furthermore, we introduce the concepts of deferred statistical Cauchy sequences and deferred statistical completeness and provide a characterization of deferred statistical summability in these spaces. As a final step, we conduct a comparative analysis of deferred statistical summability for various sequence pairs ?(?), ?(?), m(?) and n(?), under the conditions ?(?) ? m(?) < n(?) ? ?(?).

The Sturm-Liouville-Stockwell transform (SLST) is a novel addition to the class of Stockwell transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short span of time. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, this article aims to explore two other aspects of time-frequency analysis associated with SLST, namely spectral analysis associated with concentration operators and spectrogram analysis.

In this study, we discuss the approximation properties of Gamma operators G? for absolutely continuous and locally bounded functions by using results of probability theory and some inequalities with the method of Bojanic-Cheng. And then, metric form ?u (?, ?) is used with asymptotic formula combining to calculate an convergence rate asymptotically of Gamma operators G? for the bounded functions locally and also analysis techniques are used with Bojanic-Khan-Cheng?s method to calculate an optimal convergence rate of Gamma operators G? for the functions which are absolutely continuous. Lastly, the convergence of the operators to a specific function is illustrated using Maple software.

The main aim of this paper is to establish the Hyers-Ulam-Rassias and Hyers-Ulam stability of certain homogeneous and non-homogeneous impulsive Fredholm integral equations by using a fixed-point method. Both Hyers-Ulam-Rassias stability and Hyers-Ulam stability are obtained for such a class of Fredholm integral equations when considered on a finite interval. Finally four examples are presented to support the usability of our results.

For two complex unital Banach algebras A and B and a homomorphism algebra T: A ? B having the strong Riesz property, we propose a new formula for generalized Drazin T-Riesz inverses, and we give a new Laurent expansion for the resolvent of a given generalized Drazin T-Riesz invertible element. Most importantly, necessary and sufficent conditions to have the uniqueness of generalized Drazin T-Riesz inverse are given.

This paper is devoted to prove existence of renormalized solutions for a class of non-linear degenerate elliptic equations involving a non-linear convection term, which satisfies a growth properties, and a Hardy potential. Additionally, we assume that the right-hand side is anm L function, with m ? 1.

This paper introduces new classes of Finsler metrics, namely ?D-stretch metrics, isotropic ?D- stretch metrics, and relatively isotropic ?D-metrics, by exploring the Douglas curvature in Finsler geometry. The class of relatively isotropic ?D-metrics encompasses two additional classes: ?D-stretch metrics and isotropic ?D-stretch metrics. The study delves into the properties of relatively isotropic ?D-metrics, elucidating their geometric characteristics and situating them within the broader context of Finsler metrics dependent on Douglas curvature, such as Douglas or GDW-metrics. Additionally, the research investigates the interplay between relatively isotropic ?D-metrics and other key curvatures, including ?E-curvature and S-curvature, building upon prior studies on the relationships between Douglas curvature and these curvatures. Furthermore, examples of Finsler metrics are provided to elucidate the distinguishing criteria for the class of relatively isotropic ?D-metrics in comparison to well-known classes of Finsler metrics like Douglas, Weyl, and GDW-metrics.

In this article, we present and investigate new type of sequence spaces called by almost convergent Motzkin sequence spaces. We demonstrate that the newly introduced spaces are linearly isomorphic to the spaces of all almost convergent sequences and compute the ?-dual. Additionally, we characterize (M, Z) and (Z, M) for any given sequence space Z, and also determine the necessary and sufficient condition on a matrix P such that for every bounded sequence u, BM-core(Pu) ? K-core(u) and BM-core(Pu) ? st-core(u).

Dilation theory offers various structural characterizations of numerical contractions, i.e. operators whose numerical radius does not exceed one. Among these, a recent factorization result establishes that a matrix A \in M_{n \times n}(\mathbb{C}) is a numerical contraction if and only if it can be written as A = 2X*Y, where X, Y \in M_{n \times n}(\mathbb{C}) satisfy X^*X + Y^*Y = I_n . In this article, we show how an equivalent formulation of this factorization may be employed to derive new bounds for the numerical radius. The principal contributions include generalizations of several known numerical radius inequalities for Hilbert space operators, thereby extending and refining existing results in operator theory.