A NONLINEAR F-CONTRACTION FORM OF SADOVSKII'S FIXED POINT THEOREM AND ITS APPLICATION TO A FUNCTIONAL INTEGRAL EQUATION OF VOLTERRA TYPE

Kourosh Nourouzi, Faezeh Zahedi, Donal O'Regan

DOI Number
https://doi.org/10.22190/FUMI200717024N
First page
321
Last page
331

Abstract


In this paper, we give a nonlinear F-contraction form of the Sadovskii fixed
point theorem and we also investigate the existence of solutions for a functional integral equation of Volterra type.


Keywords

Fixed-point theorems, nonlinear contraction, functional integral equations

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References


A. Aghajani, J. Banas, N. Sabzali, Some generalizations of Darbo fixed point theorem and applications, Bull. Belg. Math. Soc. Simon Stevin 20, (2013), 345--358.

R.R. Akmerov, M. I. Kamenski, A.S. Potapov, A.E. Rodkina, B.N. Sadovskii, Measure of noncompactness and condensing operators, Birkhavervser Verlag, Basel (1992).

J.M. Ayerbe Toledano, T. Dominguez Benavides, G. Lopez Acedo,

Measures of noncompactness in metric fixed point theory, Operator Theory: Advances and Applications, 99. Birkhuser Verlag, Basel, 1997.

J. Banas, K. Gobel, Measures of noncompactness in Banach spaces, Lect.

Notes Pure Appl. Math., vol. 60, Dekker, New York, 1980.

J. Banas, M. Jleli, M. Mursaleen, B. Samet, C. Vetro, Advances in nonlinear analysis via the concept of measure of noncompactness. Springer, Singapore, (2017).

J. Banas, B. Rzepka, An application of a measure of noncompactness in the study of asymptotic stability, Appl. Math. Letters 16, (2003) 1-6.

J. Garcia-Falset, K. Latrach, On Darbo-Sadovskii's fixed point theorems type for abstract measures of (weak) noncompactness. Bull. Belg. Math. Soc. Simon Stevin, 22 (2015), no. 5, 797--812.

G. Darbo, Punti uniti in transformaziationi a condominio non comatto, Rend. Sem. Mat. Univ. Padova, 24 (1955) 84--92.

D. Klim, D. Wardowski, Fixed points of dynamic processes of set-valued F-contractions and application to functional equations, Fixed Point Theory Appl., 2015:22, 9 pp.

K. Kuratowski, Sur les espaces complets, Fundam. Math. 5, 301-309 (1930)

D. Wardowski, Solving existence problems via F-contractions, Proc. Amer. Math. Soc. 146 (2018), no. 4, 1585--1598.

R. Pietkun, On some generalizations of the Monch, Sadovskii and Darbo fixed point theorems. J. Fixed Point Theory Appl. 20 (2018), no. 3, Art. 95, 11 pp.

B.N. Sadovskii, A fixed-point principle, Functional Analysis and Applications, 1 (1967), no. 2, 151--153.




DOI: https://doi.org/10.22190/FUMI200717024N

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