New Fixed-Point and Common Fixed-Point Results in Finite-Dimensional Normed Pre-A∗ Vector Spaces

Kidanemariam Birhane Gebremedhin, Jonnalagadda Venkateswara Rao and Gebreslassie Tesfay Berhe

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-10

Abstract: This paper establishes new fixed-point and common fixed-point theorems for continuous and asymptotically regular self-maps defined on finite-dimensional normed pre-A∗ vector spaces over σ-complete pre-A∗-algebras. We prove that every continuous and asymptotically regular self-map on such a space has at least one fixed point (Theorem 2). Furthermore, for a pair of continuous, asymptotically regular, and r-weakly commuting self-maps satisfying a generalized contractive condition, we obtain a unique common fixed point (Theorem 3). An application to fractal image compression is presented, demonstrating how the pre-A∗ framework can model uncertainty in pixel values. These results extend classical fixed-point theory to algebraic structures where norms take values in a logical algebra rather than real numbers.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:6145269

DOI: 10.1155/ijmm/6145269

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