Fixed-Point Theorems in Branciari Distance Spaces

In this study, the concepts of σ-Caristi maps and generalized σ-contraction maps are introduced, and fixed-point theorems for such maps are established. A generalization of Caristi’s fixed-point theorem and Banach’s contraction principle is proved. The relationships among the various contraction conditions introduced in this paper are examined. Examples are provided to elucidate the main theorem, and applications to integral and differential equations are also discussed.