Open AccessOn some enriched contractions in Banach spaces and an application
Author(s) -
Pratikshan Mondal,
Hiranmoy Garai,
Lakshmi Kanta Dey
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/fil2115017m
Subject(s) - mathematics , fixed point theorem , contraction (grammar) , fixed point , uniqueness , banach space , contraction mapping , contraction principle , property (philosophy) , pure mathematics , limit (mathematics) , mathematical analysis , discrete mathematics , medicine , philosophy , epistemology
In this paper, we introduce two new types of enriched contractions, viz., enriched A-contraction and enriched A-contraction. Then we obtain fixed points of mappings satisfying such contractions using the fixed point property of the average operator of the mappings. Further, we study the well-posedness and limit shadowing property of the fixed point problem involving the contractions, and give some examples to validate the results proved. Our work improves Berinde and P?curar?s recent results on different kinds enriched contractions and some well known classical fixed point results. As an application, we prove an existence and uniqueness theorem for an integro-differential equation.