Next Article in Journal
Duality for Unified Higher-Order Minimax Fractional Programming with Support Function under Type-I Assumptions
Previous Article in Journal
Predicting Contagion from the US Financial Crisis to International Stock Markets Using Dynamic Copula with Google Trends
Previous Article in Special Issue
Modified Suzuki-Simulation Type Contractive Mapping in Non-Archimedean Quasi Modular Metric Spaces and Application to Graph Theory
Open AccessFeature PaperArticle

Ample Spectrum Contractions and Related Fixed Point Theorems

1
Department of Statistics and Operations Research, University of Granada, Granada 18010, Spain
2
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.B. 80203, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1033; https://doi.org/10.3390/math7111033
Received: 28 September 2019 / Revised: 27 October 2019 / Accepted: 28 October 2019 / Published: 2 November 2019
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, ( R , S ) -contractions and ( A , S ) -contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.
Keywords: R-function; simulation function; manageable function; fixed point; contractivity condition; binary relation R-function; simulation function; manageable function; fixed point; contractivity condition; binary relation
MDPI and ACS Style

Roldán López de Hierro, A.F.; Shahzad, N. Ample Spectrum Contractions and Related Fixed Point Theorems. Mathematics 2019, 7, 1033.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop