arXiv subjects

Fatemeh Fogh

Publications and source records attributed to Fatemeh Fogh.

4 recordsLinked to original sources

arXiv2026

T Extended Weakly Contractive, Kannan, and Geraghty Mappings Fixed Points, Equivalences,

We develop a unified T-extended framework for weakly contractive, weakly Kannan, and Geraghty classes of self-maps S on a metric space (X, d), where distances are measured on the auxiliary image via d(Tx, Ty), and the dynamics is governed by the composition of T and S. Under standard assumptions on the auxiliary map T (continuity, injectivity, subsequential convergence), fixed point theorems and Picard convergence are established for each class. The main contribution is twofold. First, it is shown that the T-extended weakly contractive class coincides with the T-extended Geraghty class, and that the T-extended weakly Kannan class coincides with the T-extended Kannan-Geraghty class. Second, the mechanism behind these equivalences is clarified by transporting the problem to an induced map F from T(X) to T(X), defined by F(Tx) = T(Sx), where the extended properties reduce exactly to the classical ones with the same control functions. A Delta-type ratio criterion on T(X) and quantitative Picard convergence rates are also provided. Examples, including Volterra smoothing operators, are presented to highlight the role of the auxiliary map. All results extend naturally to rectangular (Branciari) metric spaces.

math.FA↗

arXiv2025

Interval-Censored Survival Analysis of Grapevine Phenology: Thermal Controls on Flowering and Fruit Ripening

European grapevine (\textit{Vitis vinifera} L.) is a climate-sensitive perennial whose flowering and ripening govern yield and quality. Phenological records from monitoring programs are typically collected at irregular intervals, so true transition dates are interval-censored, and many site-years are right-censored. We develop a reproducible workflow that treats phenology as a time-to-event outcome: Status \& Intensity observations from the USA-NPN are converted to interval bounds, linked to NASA POWER daily weather, and analyzed with parametric accelerated failure time (AFT) models (Weibull and log-logistic). To avoid outcome-dependent bias from aggregating weather up to the event date, antecedent conditions are summarized in fixed pre-season windows and standardized; quality-control filters ensure adequate within-window data coverage. Applied to flowering and ripening of \textit{V.~vinifera}, the framework yields interpretable time-ratio effects and publication-ready tables and figures. Warmer pre-season conditions are associated with earlier ripening, whereas flowering responses are modest and uncertain in these data; precipitation plays, at most, a secondary role. The approach demonstrates how interval-censored survival models with exogenous weather windows can extract robust climate signals from citizen-science phenology while preserving observation uncertainty, and it generalizes readily to other species and networks.

q-bio.QM↗

arXiv2025

Isomorphisms, Moduli, and Cohomological Dimension for Twisted Triangular Banach Algebras

We introduce and study twisted triangular Banach algebras T_sigma(A,B;X), built from Banach algebras A,B, a Banach A-B bimodule X, and a pair of automorphisms sigma=(sigma_A,sigma_B). This construction extends the classical triangular framework by incorporating twisted module actions on the off-diagonal block. We obtain a complete isomorphism classification: T_sigma is isomorphic to T_tau precisely when the diagonal twists are conjugate, the bimodule admits an (alpha,beta)-equivariant isomorphism, and a shear cocycle satisfies a natural identity. In the case of group algebras, the classification detects conjugacy classes inside Aut(G), yielding new dynamical invariants absent from the untwisted setting. On the homological side, we establish sharp bounds for the Hochschild cohomological dimension and deduce that T_sigma is amenable only when X=0 and both A,B are amenable. Thus twisting enriches the classical theory while preserving extension-theoretic control of cohomology.

math.FA↗

arXiv2025

Best Proximity Points for Geraghty-Type Non-Self Mappings with a Registration-Inspired Alignment Model

We study Geraghty-type non-self mappings within the framework of best proximity point theory. By introducing auxiliary functions with subsequential convergence, we establish general conditions ensuring the existence and uniqueness of best proximity points. Our results extend and unify earlier work on proximal and Kannan-type contractions under a Geraghty setting, and we provide counterexamples showing that the auxiliary assumptions are essential. To demonstrate applicability, we construct a registration-inspired alignment model in which all hypotheses can be explicitly verified. This example illustrates how the theoretical framework guarantees a unique and well-defined alignment anchor, thereby highlighting the relevance of best proximity theory in registration problems.

math.OC↗