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Rattan Lal

Publications and source records attributed to Rattan Lal.

8 recordsLinked to original sources
arXiv2026

On the Set-Valued Katugampola Fractional Integral: Properties and Regular Selections

In this paper, we develop a theory of generalized fractional integration for set-valued mappings for the Katugampola fractional integral, which unifies the classical Riemann-Liouville and Hadamard fractional integrals. The Katugampola fractional integral of a set valued mapping is studied using integrable selections. We study its properties with respect to the Hausdorff metric on the space of nonempty compact subsets of R and several fundamental analytical characteristics including convexity, boundedness and continuity are preserved under Katugampola fractional integration. Furthermore, we establish that both bounded variation and Lipschitz regularity of a set-valued mapping are preserved under its Katugampola fractional integral. We investigate the existence of regular selections associated with the Katugampola fractional integral and show that whenever the original set valued mapping admits a selection with a specified regularity property, the corresponding Katugampola fractional integral does as well.

math.FA↗
arXiv2025

Set-Valued Fractal Approximation for Countable Data Sets

Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We first provide a construction of fractal functions for countable data sets and use these functions in the approximation and study of set-valued mappings. We also show the existence and uniqueness of an invariant Borel measure supported on the graph of a set-valued fractal function. In addition, we obtain some effective bounds on the dimensions of the constructed set-valued fractal functions.

math.FA↗
arXiv2025

Some Analytical Properties of Multivariate Fractal Functions in Lebesgue Spaces

In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to Lebesgue spaces. Then, we give analytical properties of the defined fractal operator in Lebesgue spaces. We end this article by showing the existence of Schauder basis of the associated fractal functions for the space $\mathcal{L}^q(I^n, μ_p)$.

math.FA↗
arXiv2024

Ideals in the dual of introverted subspaces of $Ψ$-pseudomeasures

Let $G$ be a locally compact group and $(Φ,Ψ)$ a complementary pair of Young functions satisfying the $Δ_2$-condition. Let $A_Φ(G)$ be the Orlicz analogue of the Figà-Talamanca Herz algebra $A_p(G).$ The dual of the algebra $A_Φ(G)$ is the space of $Ψ$-pseudomeasures, denoted by $PM_Ψ(G).$ For certain topologically introverted subspaces $\mathcal{A}$ of $PM_Ψ(G)$ and the Banach algebras $W_Φ(G)$ or $B_Φ(G),$ denoted by $\mathcal{B},$ we characterise the maximal regular left/right/two-sided ideals of the Banach algebras $\mathcal{A}^{'}$ and $\mathcal{B}^{''}$ considered with the Arens product. We further characterise the minimal left ideals of $\mathcal{A}^{'}$ and prove the necessary and sufficient conditions for the existence of minimal ideals in the algebras $A_Φ(G)$ and $\mathcal{B}.$

math.FA↗
arXiv2023

The State of Food Systems Worldwide: Counting Down to 2030

Transforming food systems is essential to bring about a healthier, equitable, sustainable, and resilient future, including achieving global development and sustainability goals. To date, no comprehensive framework exists to track food systems transformation and their contributions to global goals. In 2021, the Food Systems Countdown to 2030 Initiative (FSCI) articulated an architecture to monitor food systems across five themes: 1 diets, nutrition, and health; 2 environment, natural resources, and production; 3 livelihoods, poverty, and equity; 4 governance; and 5 resilience and sustainability. Each theme comprises three-to-five indicator domains. This paper builds on that architecture, presenting the inclusive, consultative process used to select indicators and an application of the indicator framework using the latest available data, constructing the first global food systems baseline to track transformation. While data are available to cover most themes and domains, critical indicator gaps exist such as off-farm livelihoods, food loss and waste, and governance. Baseline results demonstrate every region or country can claim positive outcomes in some parts of food systems, but none are optimal across all domains, and some indicators are independent of national income. These results underscore the need for dedicated monitoring and transformation agendas specific to food systems. Tracking these indicators to 2030 and beyond will allow for data-driven food systems governance at all scales and increase accountability for urgently needed progress toward achieving global goals.

econ.GN↗
arXiv2019

Weakly Almost Periodic and Uniformly continuous functionals on the Orlicz Figa Talamanca Herz algebras

In this paper we study weakly almost periodic and uniformly continuous functionals on the Orlicz Figà-Talamanca Herz algebras associated to a locally compact group. We show that a unique invariant mean exists on the space of weakly almost periodic functionals. We also characterise discrete groups in terms of the inclusion of the space of uniformly continuous functions inside the space of weakly almost periodic functionals.

math.FA↗