Open AccessCommon fixed point theorem for modified Kannan enriched contraction pair in Banach spaces and its applications
Author(s) -
Rizwan Anjum,
Mujahid Abbas
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/fil2108485a
Subject(s) - mathematics , fixed point , fixed point theorem , contraction (grammar) , banach space , contraction mapping , coincidence point , pure mathematics , discrete mathematics , class (philosophy) , convergence (economics) , mathematical analysis , computer science , medicine , artificial intelligence , economics , economic growth
The purpose of this paper is to introduce the class of (a,b,c)-modified enriched Kannan pair of mappings (T,S) in the setting of Banach space that includes enriched Kannan mappings, contraction and nonexpansive mappings and some other mappings. Some examples are presented to support the concepts introduced herein. We establish the existence of common fixed point of the such pair. We also show that the common fixed point problem studied herein is well posed. A convergence theorem for the Krasnoselskij iteration is used to approximate fixed points of the (a,b,c)-modified enriched Kannan pair. As an application of the results proved in this paper, the existence of a solution of integral equations is established. The presented results improve, unify and generalize many known results in the literature.