Open AccessSome Fixed Point Theorems for Almost (GF; δb)-Contractions and Application
Author(s) -
Hemant Kumar Nashine,
Ravi P. Agarwal,
Satish Shukla,
Anita Gupta
Publication year - 2017
Publication title -
fasciculi mathematici
Language(s) - English
Resource type - Journals
ISSN - 0044-4413
DOI - 10.1515/fascmath-2017-0009
Subject(s) - mathematics , metric space , fixed point , metric (unit) , fixed point theorem , discrete mathematics , point (geometry) , usability , nonlinear system , pure mathematics , mathematical analysis , computer science , geometry , physics , operations management , human–computer interaction , quantum mechanics , economics
We propose a new notion of multi-valued almost (GF; δ b )-contractions involving rational terms under δ-distance on b-metric spaces and give its relevance to fixed point results in orbitally complete b-metric spaces. An ordered version of our main result is also proved with some weaker contractive conditions. Some examples are given to show the usability of the results proved herein. Moreover, application of our result to the nonlinear integral equation is given.