Global optimal solution for a system of differential equations via measure of noncompactness
DOI:
https://doi.org/10.5269/bspm.68608Abstract
In this paper, we use a measure of noncompactness to give some best proximity point and best proximity pair results for cyclic (noncyclic) operators. As a consequence of our findings, we obtain an extension of Darbo’s fixed point theorem. Furthermore, we investigate the existence of an optimal solution for a system of ordinary differential equations as an application of our results.
References
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2. J. Banas, M. Jleli, M. Mursaleen, B. Samet, C. Vetro, Advanaces in Nonlinear Analysis via the Concept of Measure of Noncompactness. Springer, Singapore (2017).
3. J. Chen, X. Tang, Generalizations of Darbo’s fixed point theorem via simulation functions with application to functional integral equations, J. Comput. Appl. Math., 296:564–575, 2016.
4. G. Darbo, Punti uniti in transformazioni a codomino non compatto, Rend. Semin. Mat. Univ. Padova, 24:84–92, 1955.
5. A. A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Stud. Math., 171:283–293, 2005.
6. K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 112:234-240, 1969.
7. M. Gabeleh, A characterization of proximal normal structures via proximal diametral sequences, J. Fixed Point Theory Appl., 19:2909–2925, 2017.
8. M. Gabeleh, J. Markin, Optimum solutions for a system of differential equations via measure of noncompactness, Indag. Math., New Ser., 29:895–906, 2018. Filomat, 32:6087–6106, 2018.
9. V.I. Istratescu, Fixed Point Theory, Springer, Dordrecht, 1981.
10. W. A. Kirk, S. Reich, and P. Veeramani, Proximinal retracts and best proximity pairtheorems, Numer. Funct. Anal. Optim., 24:851–862, 2003.
11. K. Kuratowski, Sur les espaces completes, Fund. Math., 15:301–309, 1930.
12. B. N. Sadovskii, Limit-compact and convdensing operators, Uspehi Mat. Nauk. 27:81–146, 1972(in Russian).
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Published
2025-12-13
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Research Articles
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How to Cite
Sharma, S., & Chandok, S. . (2025). Global optimal solution for a system of differential equations via measure of noncompactness. Boletim Da Sociedade Paranaense De Matemática, 43, 1-10. https://doi.org/10.5269/bspm.68608
