Common Fixed Point Theorems via Measure of Noncompactness

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Alireza Valipour Baboli*

Abstract

In this paper, by applying the measure of noncompactness a common fixed point for the maps T and S is obtained, where T and S are self-maps continuous, commuting continuously on a closed convex subset C of a Banach space E and also S is a linear map. Then as an application, the existence of a solution of an integral equation is shown.

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Baboli, A. V. (2024). Common Fixed Point Theorems via Measure of Noncompactness. Annals of Mathematics and Physics, 7(3), 314–321. https://doi.org/10.17352/amp.000138
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Copyright (c) 2024 Baboli AV.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Darbo G. Punti uniti in trasformazioni a codominio non compatto. Rend Sem Mat Univ Padova. 1955;24:84-92. Available from: http://www.numdam.org/article/RSMUP_1955__24__84_0.pdf

Kuratowski C. Sur les espaces. Fund Math. 1930;15:301-309. Available from: https://eudml.org/doc/212357

Agarwal RP, O'Regan D. Fixed Point Theory and Applications. Cambridge University Press; 2004. Available from: https://books.google.co.in/books?id=iNccsDsdbIcC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

Aghajani A, Sabzali N. Existence of coupled fixed points via measure of noncompactness and applications. J Nonlinear Convex Anal. 2013;15(5). Available from: https://www.researchgate.net/publication/236151805_Existence_of_coupled_fixed_points_via_measure_of_noncompactness_and_applications

Akmerov RR, Kamenski MI, Potapov AS, Rodkina AE, Sadovskii BN. Measures of Noncompactness and Condensing Operators. Basel: Birkhauser-Verlag. 1992.

Banach S. On operations in abstract sets and their applications to integral equations. Fund Math. 1922;3:133-181. Available from: https://www.semanticscholar.org/paper/Sur-les-op%C3%A9rations-dans-les-ensembles-abstraits-et-Banach/ef166eb78f8e04f1d563a2622a76fd1d9e138923

Banas J, Goebel K. Measure of noncompactness in Banach Space. New York: Marcel Dekker; 1980. Available from: https://www.scirp.org/reference/referencespapers?referenceid=863695

Chang SS, Cho YJ, Huang NJ. Coupled fixed point theorems with applications. J Korean Math Soc. 1996;33(3):575-585. Available from: https://www.researchgate.net/publication/263440631_Coupled_fixed_point_theorems_with_applications

Das KM, Naik KV. Common fixed point theorem for commuting maps on a metric space. Proc Amer Math Soc. 1979;77:369-373. Available from: https://www.ams.org/journals/proc/1979-077-03/S0002-9939-1979-0545598-7/S0002-9939-1979-0545598-7.pdf

Dugundij J, Granas A. Fixed point Theory I. Warsaw: Polish Scientific Publishers. 1982. Available from: https://www.math.utep.edu/faculty/khamsi/fixedpoint/books.html

Fisher B, Sessa S. On a fixed point theorem of Gregus. Internat J Math Sci. 1986;9:23-28. Available from: http://dx.doi.org/10.1155/S0161171286000030

Fisher B. Common fixed point on a Banach space. Chuni Juan J. 1982;XI:12-15.

Gregus M Jr. A fixed point theorem in Banach space. Boll Un Mat Ital (5). 1980;17-A:193-198.

Jungck G. On a fixed point theorem of Fisher and Sessa. Internat J Math Sci. 1990;13(3):497-500. Available from: http://dx.doi.org/10.1155/S0161171290000710

Jungck G. Common fixed point for commuting and compatible maps on compacta. Proc Amer Math Soc. 1988;103:977-983. Available from: https://www.ams.org/journals/proc/1988-103-03/S0002-9939-1988-0947693-2/S0002-9939-1988-0947693-2.pdf

Aghajani A, Allahyari R, Mursaleen M. A generalization of Darbo's theorem with application to the solvability of systems of integral equations. J Comput Appl Math. 2014;260:680-770. Available from: https://doi.org/10.1016/j.cam.2013.09.039

Aghajani A, Mursaleen M, Shole Haghighi A. Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness. Acta Mathematica Scientia. 2015;35B(3):552-566. Available from: https://doi.org/10.1016/S0252-9602(15)30003-5

Aghajani A, Banas J, Sabzali N. Some generalizations of Darbo's fixed point theorem and applications. Bull Belg Math Soc Simon Stevin. 2013;20(2):345-358. Available from: http://dx.doi.org/10.36045/bbms/1369316549

Jungck G. Compatible mappings and common fixed points. Internet J Math Sci. 1986;9:771-779. Available from: https://doi.org/10.1155/S0161171286000935

Jungck G. Compatible mappings and common fixed points (2). Internat J Math Sci. 1988;11(2):285-288. Available from: http://dx.doi.org/10.1155/S0161171288000341

Jungck G. Commuting mappings and fixed points. Am Math Monthly. 1976;83:261-263. Available from: http://dx.doi.org/10.2307/2318216

Khamsi MA, Kirk WA. An Introduction to Metric Spaces and Fixed Point Theory. Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs, and Texts. 2001. Available from: https://www.amazon.in/Introduction-Metric-Spaces-Applied-Mathematics/dp/0471418250

Kirk WA. A fixed point theorem for mappings which do not increase distances. Amer Math Monthly. 1965;72:1004-1006. Available from: http://dx.doi.org/10.2307/2313345

Rudin W. Real and Complex Analysis. McGraw-Hill; 1966. Available from: https://59clc.wordpress.com/wp-content/uploads/2011/01/real-and-complex-analysis.pdf

Sessa S. On a weak commutativity condition of mappings in fixed point considerations. Publ Inst Math. 1982;32(46):149-153. Available from: https://eudml.org/doc/254762

Srivastava R, Jain N, Qureshi K. Compatible mapping and common fixed point theorem. IOSR J Math. 2013;7(1):46-48. Available from: https://www.iosrjournals.org/iosr-jm/papers/Vol7-issue1/G0714648.pdf

Wong CS. On Kannan maps. Proc Amer Math Soc. 1975;47:105-111. Available from: https://typeset.io/pdf/on-kannan-maps-ywodhke8zo.pdf