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

2025/10/02 by Fatemeh Fogh, Fogh, Fatemeh, Sara Behnamian +1
Computer Science · Mathematics · #Constraint Satisfaction and Optimization #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2510.02406

openalex publication_date 2025/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Two Fixed-Point Theorems For Special Mappings
• Kannan Fixed-Point Theorem On Complete Metric Spaces And On Generalized Metric Spaces Depended an Another Function

Related

• Best proximity points for proximal contractions
• A note on the paper "Best proximity point of generalized F-proximal\n non-self contractions
• Proximal quasi-normal structure and existence of best proximity points
• Best proximity point of generalized θ-ϕ-proximal non-self contractions
• A note on best proximity point for proximal contraction