Common fixed point theorems under (R,S)$(R,\mathcal {S})$-contractivity conditions
نویسنده
چکیده
*Correspondence: [email protected] 1Department of Quantitative Methods for Economics and Business, University of Granada, Granada, Spain Full list of author information is available at the end of the article Abstract Very recently, Roldán-López-de-Hierro and Shahzad introduced the notion of R-contractions as an extension of several notions given by different researchers (for instance, R-contractions generalize Meir-Keeler contractions, Z-contractions involving simulation functions by Khojasteh et al., manageable contractions by Du and Khojasteh, Geraghty’s contractions, Banach contractions, etc.). In this manuscript, we use R-functions to present existence and uniqueness coincidence (and common fixed) point results under a contractivity condition that extend some celebrated contractive mappings. In our main theorems, we employ a binary relation on the metric space, which does not have to be a partial order. Finally, we illustrate our technique with an example in which other previous statements cannot be applied: in fact, we show how to apply our main results to a new kind of contractivity conditions which cannot be expressed in separate variables.
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