Axioms (Dec 2023)

On Some Properties of Multi-Valued Feng–Liu-Type Operators in Metric Spaces

  • Adrian Petruşel,
  • Gabriela Petruşel,
  • Lijun Zhu

DOI
https://doi.org/10.3390/axioms13010024
Journal volume & issue
Vol. 13, no. 1
p. 24

Abstract

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In the context of a complete metric space, the most important fixed-point result for multi-valued operators was given in 1969. Many extensions of this fixed-point principle for multi-valued operators were proved by different authors. Based on some of the above-mentioned results, we introduce the notion of the multi-valued Feng–Liu-type operator and we construct an abstract fixed-point theory for this general class of multi-valued operators. Our results extend and complement some theorems in metric fixed-point theory for multi-valued operators. An application to a Cauchy problem related to a first-order differential inclusion is also given. In this case, our theorem improves several previous theorems on this subject by relaxing the contraction-type condition (with respect to its second argument) on the multi-valued right-hand side.

Keywords