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Invariant approximation in 2-banach space with \(H^{+}\) mappings

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Abstract

In order to study the invariant approximation in 2-Banach spaces, we define the concept of \( H^{+} \) type nonexpansive mapping to investigate the existence and uniqueness of approximation. Using \( H^{+} \) type non expansive multi-valued mapping in 2-Banach spaces to obtain a generalization of the classical Nadler’s fixed point theorem, also discuss the invariant approximation and prove several new results by replacing multi-valued mapping with \( H^{+} \) mapping in 2-Banach space.

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  1. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai, 600 005, India

    M. Pitchaimani & K. Saravanan

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  1. M. Pitchaimani
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  2. K. Saravanan
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Pitchaimani, M., Saravanan, K. Invariant approximation in 2-banach space with \(H^{+}\) mappings. Afr. Mat. 35, 28 (2024). https://doi.org/10.1007/s13370-024-01169-6

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