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Prešić type results in 2-Banach spaces

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Abstract

In this paper, we generalize the Banach contraction principle by proving common fixed point theorems for mappings satisfying Prešić type conditions in 2-Banach spaces. The common fixed point is approximated by the \(k\)-Picard type and \(k\)-Mann type iteration schemes in product spaces. The results in this paper extend the results of Prešić in the framework of a 2-Banach space. An example is provided which illustrate the results.

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Acknowledgments

The author is thankful to the reviewers and Professor Stojan Radenović for their useful comments and suggestions on this paper.

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  1. Department of Applied Mathematics, Shri Vaishnav Institute of Technology and Science, Gram Baroli Sanwer Road, Indore, 453331, Madhya Pradesh, India

    Satish Shukla

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  1. Satish Shukla
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Correspondence to Satish Shukla.

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Shukla, S. Prešić type results in 2-Banach spaces. Afr. Mat. 25, 1043–1051 (2014). https://doi.org/10.1007/s13370-013-0174-2

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