Conceptual

Fixed-Point Theorems in Semimetric Spaces with Triangle Functions

An extension of classical contraction-mapping fixed-point theory beyond metric spaces to semimetric spaces whose generalized triangle inequality is governed by a triangle function (the Bessenyei-Pales framework). General theorems for weak, partial, Bianchini, and Chatterjea-Bianchini contractions are established and then specialized to metric, b-metric, ultrametric, and power-triangle distance spaces, yielding new existence and uniqueness results for weak and partial contractions.