C*-algebra-valued Measure of Non-compactness with Applications


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Authors

  • Fouzia Shaheen United Arab Emirates University

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).

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Published

2023-10-18

How to Cite

Shaheen, F. (2023). C*-algebra-valued Measure of Non-compactness with Applications. Results in Nonlinear Analysis, 6(4), 30–39. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/132