DOI: 10.24193/fpt-ro.2024.1.21

Authors: Sajad Ranjbar

Abstract: In this paper, we investigate the nonemptiness and boundedness of the set of zeros of a monotone operator in Hadamard spaces. Two coercivity conditions R1 and R2 are proposed. The equivalence between the nonemptiness of the set of zeros of a monotone operator and coercivity condition R1 is established. Moreover, it is shown that coercivity condition R2 is a sufficient and necessary condition for the boundedness of the set of zeros of a monotone operator. Some applications in convex minimization and fixed point theory are also presented to support the main results.

Key Words and Phrases: Inclusion problems, monotone operators, coercivity conditions, fixed point, nonemptiness and boundedness of the set of zeros, Hadamard spaces.

2010 Mathematics Subject Classification: 47H05, 47H10, 47J05, 47J20.

Published on-line: February 1st, 2024.

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