C*-algebra-valued Measure of Non-compactness with Applications
Abstract views: 189 / PDF downloads: 90
Keywords:
Fixed point, Measure of non-compactness, Darbo fixed point theorem, C*-algebra valued measure of non-compactness.Abstract
In this article a novel concept of C*-algebra-valued measure of non- compactness is defined. Using this concept, the well known fixed point the- orems of Darbo, Sadowskii and Krasnoslskii are generalized. We present non-trivial examples and applications to validate the real utilization of our results.
References
Smart DR., Fixed point theorems. Cup Archive; (1980).
Darbo G., Punti uniti in trasformazioni a codominio non compatto. Rendiconti del Seminario matematico della
Università di Padova. 24, (1955), 84–92.
Kuratowski, K., “Sur les espaces complets,” Fundamenta Mathematicae, 15 (1), (1930), 301–309.
Istrătescu VI. On a measure of non-compactness. Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. 16 (2), (1972), 195–7.
Akhmerov, R., Kamenskii, M. I., Potapov, A. S., Rodkina, A. E., Sadovskii, B. N., “Measures of non-compactness and
condensing operators,” in Operator Theory: Advances and Applications, A. Iacob, Ed.,vol. 55, Basel, Switzerland, Basel, Birkhauser, (1992).
Appell, J., “Measures of non-compactness, condensing operators and fixed points: an application-oriented survey,” Fixed PointTheory, 6 (2), (2005), 157–229.
Banas, J., Goebel, K., Measures of Non-compactness in Banach Spaces, vol. 60 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, (1980).
Aghajani, A. Allahyari, R. Mursaleen, M., “A generalization of Darbo’s theorem with application to the solvability of
systems of integral equations,” Journal of Computational and Applied Mathematics, 260, (2014), 68–77.
Ahmad, N., Al-Rawashdeh, A., Mehmood, N., Radenović, S., Fixed points of monotone mappings via generalized-measure of non-compactness. Vietnam Journal of Mathematics, 50(1), (2022), 275–285.
Jleli M, Mursaleen M, Sadarangani K, Samet B. A cone measure of non-compactness and some generalizations of
Darbo’s theorem with applications to functional integral equations. Journal of Function Spaces. 2016, (2016).
Sadowski BW. Limit-compact and condensing operators. Russian Math. Surveys. 27, (1972), 85–155.
Al-Rawashdeh, A., Shatanawi, W., Khandaqji, M. Normed Ordered and E-Metric Spaces. International Journal of
Mathematics and Mathematical Sciences. Volume 2012, Article ID 272137, 11 pages. doi:10.1155/2012/272137
Mehmood, N., Al Rawashdeh, A., Radenović, S., New fixed point results for E-metric spaces, Positivity 23 (5), (2019), 1101–1111.
Kutbi, M. A., Ahmad, J., Azam, A., Al-Rawashdeh, A.S., Generalized common fixed point results via greatest lower
bound property, Journal of Applied Mathematics, 2014, (2014), 265865.
Ma, ZH, Jiang, LN, Sun, H K., C*-Algebras-valued metric spaces and related fixed point theorems. Fixed Point Theory Appl. 2014, (2014), 206.
Banas’ J, Jleli M, Mursaleen M, Samet B, Vetro C, editors. Advances in nonlinear analysis via the concept of measure of non-compactness. Singapore: Springer Singapore; (2017).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Results in Nonlinear Analysis
This work is licensed under a Creative Commons Attribution 4.0 International License.