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2025-12-31
Patrik Peška, Lenka Vítková, Josef Mikeš
In this work, the fundamental equations of generalized $\varphi(Ric)$-vector fields in both classical and hyperbolic K\"ahler spaces are derived and expressed as systems of linear partial differential equations in the Cauchy-type covariant derivative. Additionally, the specific form of the Ricci tensor $Ric$ for these spaces is determined.
2025-12-31
Mahamed Beghdadi, Bilel Krichen
In this paper, we define a new part of spectrum called the essential $\overline{\gamma}$-pseudospectrum of a linear operator via the measure of noncompactness of Kuratowski $\overline{\gamma}$. Our aim is to characterize the essential $\overline{\gamma}$-pseudospectrum of a bounded (an unbounded) linear operator. Moreover, we study the invariance of the $\overline{\gamma}$-pseudospectrum under perturbations.
2025-12-31
Pinnangudi N. Natarajan, Ants Aasma
Let $\K$ be a complete, non-trivially valued, ultrametric (or non-archimedean) field, and $\lambda = \{\lambda_n\}$ be a sequence in $\K$ with the property $0 < |\lambda_n| \nearrow \infty, n \to \infty$, i.e., the speed of convergence. In this paper, we study the speed-Maddox spaces over$\K$, defined by the parameter $\lambda$, and investigate their structure for paranormally $\lambda$-zero-convergent, paranormally $\lambda$-convergent, and paranormally $\lambda$-bounded sequences. Earlier, in classical cases, the matrix transforms between different Maddox spaces have been widely investigated. In the present paper necessary and sufficient conditions are found for a matrix $A$ over $\K$ to transform all paranormally $\lambda$-zero-convergent or all paranormally $\lambda$-convergent sequences into the spaces of all paranormally $\mu$-zero-convergent, all paranormally $\mu$-convergent or all paranormally $\mu$-bounded sequences, where $\mu$ is another speed of convergence in $\K$. As an application of main results, one example where $A$ is the Srinivasan summation method $Y$ is presented.
2025-12-31
Sayed Khalil Ekrami
Let $ \mathcal{M} $ be a Hilbert C$ ^* $-module and $ \sigma, \tau $ be two Hilbert C$ ^* $-module homomorphisms on $ \mathcal{M} $. As a generalization of Hilbert C$ ^* $-module higher derivations on $ \mathcal{M} $, we consider the sequence of linear mappings $ \{\Phi_n \}_{n=0}^\infty$ satisfying the equation \[ \Phi_n (\langle a,b \rangle c) =\sum_{i+j+k=n}\big\langle \Phi_i \big(\sigma^{n-i}(a)\big),\Phi_j\big(\sigma^k\tau^i(b)\big)\big\rangle \Phi_k\big(\tau^{n-k}(c)\big) \] for all $ a,b,c \in \mathcal{M} $ and each non-negative integer $ n $. Such a sequence $ \{\Phi_n \}_{n=0}^\infty$ is called Hilbert C$ ^* $-module higher ($\sigma, \tau$)-derivation on $ \mathcal{M} $. In this paper, we show that under some conditions, every Hilbert C$ ^* $-module Jordan higher ($\sigma, \tau$)-derivation on $ \mathcal{M} $, is a Hilbert C$ ^* $-module higher ($\sigma, \tau$)-derivation. As a consequence, we show that under the same conditions, every Hilbert C$ ^* $-module Jordan ($\sigma, \tau$)-derivation on $ \mathcal{M} $, is a Hilbert C$ ^* $-module ($\sigma, \tau$)-derivation.
2025-12-31
Canan Hazar Güleç, Özlem Girgin Atlıhan
Paranormed linear spaces have many important properties, since they appear as the generalizations of normed linear spaces. The most well-known paranormed linear P space among these spaces is ℓ(p) space of the sequences x=(x_{k}) satisfying ∑_{k=0}^{∞}|x_{k}|^{p_{k}}<∞ , which was defined by Maddox in 1967. The main purpose of this study is to introduce a new paranormed space |Υ_{u}^{r}|(p) over the paranormed space ℓ(p) using the Jordan totient mean that is a well-known arithmetic function in number theory, where p=(p_{k}) is a bounded sequence of positive real numbers. Besides this, we investigate some topological properties of this space and determine its α-,β-, and γ- duals. Finally, we characterize the classes of infinite matrices (|Υ_{u}^{r}|(p),λ) and (λ,|Υ_{u}^{r}|(p)), where λ is any given sequence space.