http://localhost:8080/xmlui/handle/123456789/12 Thu, 13 Aug 2026 20:46:05 GMT 2026-08-13T20:46:05Z http://localhost:8080/xmlui/handle/123456789/12819 Optimal Transport and Convexity in Orlicz Spaces Mogoi, Evans; Obogi, Robert Karieko Optimal transport theory has traditionally been developed in the context of classical spaces, where Wasserstein metrics provide a natural geometry on the space of probability measures with finite -moments. However, in many applications-such as in finance, statistical mechanics, and the modelling of heavy-tailed phenomena-classical spaces prove insufficient. This paper proposes a novel generalization of optimal transport to Orlicz spaces, which naturally extend the framework by accommodating more general growth conditions via Young functions. We introduce and rigorously define the Wasserstein-Orlicz metric and explore its topological and geometric properties on spaces of probability measures with finite Orlicz norm. Key results include the extension of Kantorovich duality to the Orlicz setting, as well as the derivation of convexity and lower semicontinuity properties of entropytype functionals under the Wasserstein-Orlicz geometry. Applications are presented in the context of stochastic processes with heavy-tailed distributions, where the classical assumptions of finite p-moments are violated. The proposed framework opens a new avenue for analysing optimal transport problems in nonstandard settings and provides tools for applications in areas where data exhibits non-Gaussian behaviour. Tue, 30 Jun 2026 00:00:00 GMT http://localhost:8080/xmlui/handle/123456789/12819 2026-06-30T00:00:00Z http://localhost:8080/xmlui/handle/123456789/12669 Stability of Semigroups of Linear Operators in Variable Banach Spaces Obogi, Robert Karieko; Mogoi N, Evans This paper develops a theory for stability analysis of semigroups of linear operators acting on variable Banach spaces—families of Banach spaces {X(t)}t≥0 whose norms may depend on time. We establish generation theorems under appropriate resolvent conditions, characterize exponential stability through Lyapunov-type functionals, and analyze spectral properties of evolution families in variable settings. Our approach systematically extends classical semigroup theory to accommodate time-dependent norms by transporting all objects to a fixed reference space. Applications include non-autonomous parabolic equations and reaction-diffusion systems with time-dependent coefficients. All proofs are provided with full mathematical rigor, addressing technical challenges unique to variable Banach spaces Mon, 30 Mar 2026 00:00:00 GMT http://localhost:8080/xmlui/handle/123456789/12669 2026-03-30T00:00:00Z http://localhost:8080/xmlui/handle/123456789/11329 Duality and Weak Compactness in Generalized Orlicz-Bochner Spaces with Applications to Operator Equations Obogi, Robert Karieko In this paper, we investigate the duality structure and weak compactness properties of generalized Orlicz–Bochner spaces LΦ(X,µ;E), where (X,µ) is a finite measure space, E is a Banach space, and Φ is a convex modular function satisfying a generalized ∆2 -condition. Unlike classical Lebesgue and Bochner spaces, these spaces accommodate variable nonlinearity and non-standard growth, thus providing a more flexible functional analytic framework for studying nonlinear phenomena. We first characterize the dual of LΦ(X,µ;E) under modular convergence and develop criteria for reflexivity and weak compactness based on modular and geometric conditions on Φ and E. Furthermore, we establish sufficient conditions for the compactness and continuity of integral operators acting on these spaces. As an application, we analyze the solvability of nonlinear operator equations and integrodifferential equations with kernel-type operators, where standard Lp or Sobolev methods fail. Our results extend classical duality and compactness theory and open new avenues for solving evolution equations in variable exponent and Orlicz-type frameworks. Wed, 31 Dec 2025 00:00:00 GMT http://localhost:8080/xmlui/handle/123456789/11329 2025-12-31T00:00:00Z http://localhost:8080/xmlui/handle/123456789/10691 Norm attainment and structural properties in Orlicz spaces: A comprehensive study on strict convexity, duality, and optimization Mogoi, N. Evans; Obogi, Robert We investigate norm attainability and duality properties in Orlicz spaces, extending classical results from Banach and Hilbert spaces to a more gen eral functional framework. We establish 14 fundamental theorems that character ize norm attainment in terms of strict convexity, uniform convexity, and weak con vergence. We explore the duality structure of Orlicz spaces, highlighting key differ ences from Lp spaces and providing a variational characterization of the norm. We also discuss applications in optimization and variational problems, demonstrating the significance of norm-attaining functionals in these settings. Our findings con tribute to a deeper understanding of Orlicz space geometry and its implications for functional analysis and applied mathematics. Wed, 01 Jan 2025 00:00:00 GMT http://localhost:8080/xmlui/handle/123456789/10691 2025-01-01T00:00:00Z