Fixed point results for multipoint Kannan-type mappings

2025/04/19 by Bisht, Ravindra K., Petrov, Evgeniy
#FOS: Mathematics #General Topology (math.GN) #Primary 47H10 #Secondary 47H09

paper · doi:10.48550/arxiv.2504.14213

Abstract

We introduce and study a new type of mappings in metric spaces termed n-point Kannan-type mappings. A fixed-point theorem is proved for these mappings. In general case such mappings are discontinuous in the domain but necessarily continuous at fixed points. Conditions under which usual Kannan mappings and mapping contracting the total pairwise distances between n points are n-point Kannan-type mappings are found. It is shown that additional conditions of asymptotic regularity and continuity allow to extend the value of the contraction coefficient in fixed-point theorems for n-point Kannan-type mappings.

Related

• A Fixed Point Theorem for Kannan-type Maps in Metric Spaces
• Kannan Fixed-Point Theorem On Complete Metric Spaces And On Generalized Metric Spaces Depended an Another Function
• More general contractions in perturbed metric spaces
• An extension of Mizoguchi-Takahaashi's fixed point theorem
• A three point extension of Chatterjea's fixed point theorem with at most two fixed points