Fixed-Point Theorems for Multivalued Weak-Type Contractions in Metric Spaces
DOI:
https://doi.org/10.33003/Keywords:
metric spaces, contraction mappings, weak contraction, multi-valued contraction, fixed pointAbstract
This paper introduces the notion of weak multi-valued contraction mapping in the context of metric spaces and examines whether fixed points exist for such contractions under certain appropriate assumptions. A few implications in single-valued mappings are found. New multi-valued analogs of the fixed-point theorems presented here are deduced as corollaries because the fixed point of a single-valued mapping satisfying the weak contractive condition is not always unique, making the concepts more appropriate for fixed point theorems of multi-valued functions. Furthermore, non-trivial instances are given to demonstrate the validity of our findings.
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