Some New Results for (α, β)-Admissible Mappings in 𝔽-Metric Spaces with Applications to Integral Equations

Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as Banach spaces and algebras, with minimal conditions and structures, transcending in this way the numerical underlying scenario. This is performed via fixed point of an operator defined on a b-metric space of Banach-valued functions with domain on a real interval. The sets of images may provide uniparametric fractal collections of measures, operators or matrices, for instance. The defining operator is linked to a collection of maps (or iterated function system, and the conditions on these mappings determine the properties of the fractal function. In particular, it is possible to define continuous curves and fractal functions belonging to Bochner spaces of Banach-valued integrable functions. As residual result, we prove the existence of fractal functions coming from non-contractive operators as well. We provide new constructions of bases for Banach-valued maps, with a particular mention of spanning systems of functions valued on C*-algebras.

Section: Fractal Interpolation In Banach Spaces and Algebrasmentioning

confidence: 99%

Fractal Curves on Banach Algebras

Navascués

2022

“…These novel functions provide even greater adaptability and enable fixed point analysis within broader and more diverse mathematical structures. For a deeper exploration of these advancements and their implications, readers are encouraged to delve into references [12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Theorems: Exploring Applications in Fractional Differential Equations for Economic Growth

Abdou

2024

The aim of this research is to introduce two new notions, Θ-(Ξ,h)-contraction and rational (α,η)-ψ-interpolative contraction, in the setting of F-metric space and to establish corresponding fixed point theorems. To reinforce understanding and highlight the novelty of our findings, we provide a non-trivial example that not only supports the obtained results but also illuminates the established theory. Finally, we apply our main result to discuss the existence and uniqueness of solutions for a fractional differential equation describing an economic growth model.

“…Afterwards, Hussain et al [10] studied the solution for a differential equation by obtaining some new results in this direction. Subsequently, Asif et al [11] and Faraji et al [12] presented fixed point theorems in F-MSs and investigated the solutions of integral equations. Kanwal et al [13] made a significant contribution by merging the concepts of F-MSs and orthogonal sets.…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Results with Applications to Fractional Differential Equations of Anomalous Diffusion

Ma,

Zahed,

Ahmad

2024

The main objective of this manuscript is to define the concepts of F-(⋏,h)-contraction and (α,η)-Reich type interpolative contraction in the framework of orthogonal F-metric space and prove some fixed point results. Our primary result serves as a cornerstone, from which established findings in the literature emerge as natural consequences. To enhance the clarity of our novel contributions, we furnish a significant example that not only strengthens the innovative findings but also facilitates a deeper understanding of the established theory. The concluding section of our work is dedicated to the application of these results in establishing the existence and uniqueness of a solution for a fractional differential equation of anomalous diffusion.