DOI: 10.24193/fpt-ro.2025.2.18

Authors: V. Pragadeeswarar and R. Gopi

Abstract: In this present work, we define the notion of proximally generalized nonexpansive and proximally quasi-contractions in case of multi-valued non-self mappings. Using projective operator, we propose Mann's iteration and Ishikawa's iteration associated with multi-valued non-self mappings in the setting of Banach space. Through the proposed iterative processes, we approximate best proximity point of multi-valued non-self mappings under certain assumptions.

Key Words and Phrases: Multi-valued mappings, Mann's iteration, Ishikawa's iteration, fixed points, best proximity points.

2010 Mathematics Subject Classification: 47H10, 46B20, 54H25.

Published on-line: May 1st, 2025.

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