TY - JOUR
ID - 17869
TI - On Unique Solutions of Integral Equations by Progressive Contractions
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Tunc, Osman
AU - Graef, J. R.
AU - Tunc, Cemil
AD - Department of Computer Programming, Baskale Vocational School, Van Yuzuncu Yil University, 65080, Campus, Van, Turkey.
AD - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA.
AD - Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey.
Y1 - 2024
PY - 2024
VL -
IS -
SP -
EP -
KW - existence
KW - uniqueness
KW - Hammerstein integral equation
KW - Fixed point
KW - progressive contractions
DO - 10.22034/cmde.2024.59214.2516
N2 - The authors consider Hammerstein type integral equations for the purpose of obtaining new results on the uniqueness of solutions on an infinite interval. The approach used in the proofs is based on the technique called progressive contractions due to T. A. Burton. Here, the authors apply Burton's method to a general Hammerstein type integral equation that also yields existence of solutions. In much of the existing literature, investigators prove uniqueness of solutions of integral equations by applying some type of fixed point theorem. This can prove to be a difficult process that sometimes involves patching together solutions on short intervals and perhaps involving translations. In this paper, using progressive contractions in three simple short steps, each one being an elementary contraction mapping on a short interval, the authors improve the technique due to Burton by considering a general Hammerstein type integral equation, and they obtain the uniqueness of solutions on an infinite interval.
UR - https://cmde.tabrizu.ac.ir/article_17869.html
L1 - https://cmde.tabrizu.ac.ir/article_17869_b91b2eed55aa41016212c6aadc804bae.pdf
ER -