Open AccessGlobal optimal approximate solutions of best proximity points
Author(s) -
Mohammad Reza,
Vahid Parvaneh,
M. Mursaleen
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2105555h
Subject(s) - mathematics , uniqueness , contraction (grammar) , contraction mapping , fixed point , contraction principle , convergence (economics) , usability , discrete mathematics , pure mathematics , mathematical analysis , computer science , medicine , economics , economic growth , human–computer interaction
In this paper, we introduce the concept of contractive pair maps and give some necessary and sufficient conditions for existence and uniqueness of best proximity points for such pairs. In our approach, some conditions have been weakened. An application has been presented to demonstrate the usability of our results. Also, we introduce the concept of cyclic ?-contraction and cyclic asymptotic ?-contraction and give some existence and convergence theorems on best proximity point for cyclic ?-contraction and cyclic asymptotic ?-contraction mappings. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory.