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\(\varvec{\varphi }\)-admissibility results via extended simulation functions

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Abstract

We introduce the class of extended simulation functions, which is more large than the class of simulation functions, recently introduced in (Khojasteh et al. Filomat 29(6):1189–1194, 2015). We obtain a \(\varphi \)-admissibility result involving extended simulation functions, for a new class of mappings \(T: X\rightarrow X\), with respect to a lower semi-continuous function \(\varphi : X\rightarrow [0,\infty )\), where X is a set equipped with a certain metric d. The main theorem in this paper generalizes a recent \(\varphi \)-admissibility result obtained in (Karapınar et al. Fixed Point Theory Appl 2015:152, 2015), and many other related results.

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Acknowledgements

A.F. Roldán López de Hierro is grateful to the Department of Quantitative Methods for Economics and Business of the University of Granada. The same author has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE. Bessem Samet would like to extend his sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the International Research Group Project No. IRG14-04.

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Authors and Affiliations

  1. Department of Quantitative Methods for Economics and Business, University of Granada, Granada, Spain

    A. F. Roldán López de Hierro

  2. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455 , Riyadh, 11451, Saudi Arabia

    Bessem Samet

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  1. A. F. Roldán López de Hierro
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  2. Bessem Samet
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Correspondence to Bessem Samet.

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de Hierro, A.F.R.L., Samet, B. \(\varvec{\varphi }\)-admissibility results via extended simulation functions. J. Fixed Point Theory Appl. 19, 1997–2015 (2017). https://doi.org/10.1007/s11784-016-0385-x

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  • DOI: https://doi.org/10.1007/s11784-016-0385-x

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