Best Proximity Point Results for Generalization of α ̌–η ̌ Proximal Contractive Mapping in Fuzzy Banach Spaces

Raghad I. Sabri, Buthainah A. Ahmed


The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems provide an approximate solution to the fixed-point equation Tҳ = ҳ. It is used to solve the problem to determine an approximate solution that is optimum. The main goal of this paper is to present new types of proximal contraction for nonself mappings in a fuzzy Banach space. At first, the notion of the best proximity point is presented. We introduce the notion of α ̌–η ̌-β ̌ proximal contractive. After that, the best proximity point theorem for such type of mappings in a fuzzy Banach space is proved. In addition, the concept of α ̌–η ̌-φ ̌ proximal contractive mapping is presented in a fuzzy Banach space and under specific conditions, the best proximity point theorem for such type of mapping is proved. Additionally, some examples are supplied to show the results' applicability.


α ̌–η ̌-β ̌ proximal contractive mapping; α ̌–η ̌-φ ̌ proximal contractive; Best proximity point; Best proximity point theorem; Fuzzy normed space

Full Text:




  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.


The Indonesian Journal of Electrical Engineering and Computer Science (IJEECS)
p-ISSN: 2502-4752, e-ISSN: 2502-4760
This journal is published by the Institute of Advanced Engineering and Science (IAES) in collaboration with Intelektual Pustaka Media Utama (IPMU).

shopify stats IJEECS visitor statistics