Best proximity point theorems for p-proximal \alpha,\eta,\beta-quasi contractions in metric spaces with w0-distance
Received:December 31, 2020  Revised:August 14, 2021
Key Word: Best proximity point   p-proximal \alpha,\eta,\beta-quasi contraction   w0-distance   \alpha-proximal admissible mapping with respect to \eta   (\alpha   d) regular mapping with respect to \eta
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.\,11701259, 11461045, 11771198, 11361042) and Jiangxi Provincial Natural Science Foundation (Grant No.\,20202BAB201001).
 Author Name Affiliation Address Mengdi Liu Nanchang University Xuefu Road 999, Honggu new district Zhaoqi Wu Nanchang University Xuefu Road 999, Honggu new district Chuanxi Zhu Nanchang University Xuefu Road 999, Honggu new district Chenggui Yuan Swansea University Singleton Park, SA2 8PP, UK
Hits: 30
In this paper, we propose a new class of non-self mappings called $p$-proximal $\alpha$-$\eta$-$\beta$-quasi contraction, and introduce the concepts of $\alpha$-proximal admissible mapping with respect to $\eta$ and $(\alpha,d)$ regular mapping with respect to $\eta$. Based on these new notions, we study the existence and uniqueness of best proximity point for this kind of new contractions in metric spaces with $w_0$-distance and obtain a new theorem, which generalize and complement the results in [Ayari, M. I. et al. {\it Fixed Point Theory Appl.}, 2017, 2017: 16] and [Ayari, M. I. et al. {\it Fixed Point Theory Appl.}, 2019, 2019: 7]. We give an example to show the validity of our main result. Moreover, we obtain several consequences concerning about best proximity point and common fixed point results for two mappings, and we present an application of a corollary to discuss the solutions to a class of systems of Volterra type integral equations.