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Simulation functions: a survey of recent results

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

This article surveys many of the recent works regarding simulation functions and \(\mathcal {Z}\)-contractions that came into existence after the publication of Khojasteh et al. (Filomat 29(6):1189–1194, 2015). These results assess inclusive of simulation functions, \(\mathcal {Z}\)-contractions, b-simulation functions, Suzuki-type \(\mathcal {Z}\)-contractions, Darbo’s fixed point theorem, \(\alpha \)-admissible \(\mathcal {Z}\)-contractions, first-order periodic problems and variational inequality problems. Additionally, we consider many of the metric frameworks that have been taken into account while exploring the results.

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Acknowledgements

The authors gratefully acknowledge the referee(s) for constructive comments and suggestions which have reasonably improved the first as well as the revised version of this article. We also like to thank Hiranmoy Garai for his helps in constructing examples during the first revision of the article. The first named author would like to convey his cordial thanks to DST-INSPIRE, New Delhi, India for their financial supports under INSPIRE fellowship scheme.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, India

    Ankush Chanda & Lakshmi Kanta Dey

  2. Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia

    Stojan Radenović

  3. Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia

    Stojan Radenović

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  1. Ankush Chanda
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  2. Lakshmi Kanta Dey
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  3. Stojan Radenović
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Correspondence to Lakshmi Kanta Dey.

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Chanda, A., Dey, L.K. & Radenović, S. Simulation functions: a survey of recent results. RACSAM 113, 2923–2957 (2019). https://doi.org/10.1007/s13398-018-0580-2

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