An Enhanced Darbo-Type Fixed Point Theorems and Application to Integral Equations
Keywords:
Generalized Operator, Existence Theory, Integral Equations, Differential Equations, Measure of Noncompactness, Banach Spaces, Functional Equations, Mathematical Structures, Solution Guarantees, Theoretical MathematicsAbstract
This manuscript introduces a generalized operator and presents new Darbo-type fixed point theorems pivotal in the existence theory of integral and differential equations. The significance of these theorems lies in their ability to provide conditions under which solutions to complex mathematical problems can be guaranteed. We establish our results by employing the measure of noncompactness within the context of Banach spaces, a framework that allows for a comprehensive analysis of functional equations. Our findings extend existing Darbo-type fixed point theorems and offer a deeper understanding of the underlying mathematical structures. By generalizing these results, we contribute to the broader field of fixed-point theory, enhancing its applicability to various mathematical disciplines. The implications of our work are substantial, as they facilitate the development of new methods for solving integral and differential equations that arise in both theoretical and applied contexts.
Downloads
References
REFERENCES
Darbo, G. (1955). Punti uniti in trasformazioni a codominio non compatto. Rendiconti del Seminario matematico della Università di Padova, 24, 84-92.
Arab, R. (2015). Some fixed point theorems in generalized Darbo fixed point theorem and the existence of solutions for system of integral equations. Journal of the Korean Mathematical Society, 52(1), 125-139.
Mahato, R. K., Mahato, N. K. (2021). Existence solution of a system of differential equations using generalized Darbo’s fixed point theorem. AIMS Mathematics, 6(12), 13358-13370.
Beloul, S., Mursaleen, M., Ansari, A. H. (2021). A generalization of Darbo’s fixed point theorem with an application to fractional integral equations. J. Math. Ineq, 15, 911-921.
Parvaneh, V., Khorshidi, M., De La Sen, M., Işık, H., Mursaleen, M. (2020). Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations. Advances in Difference Equations, 2020(1), 1-13.
Nikam, V., Shukla, A. K., & Gopal, D. (2023). Existence of a system of fractional order differential equations via generalized contraction mapping in partially ordered Banach space. International Journal of Dynamics and Control, 1-11.
Banaś, J. (1980). On measures of noncompactness in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, 21(1), 131-143.
Nikam, V., Shukla, A. K., Gopal, D., & Sumalai, P. Some Darbo‐type fixed‐point theorems in the modular space and existence of solution for fractional ordered 2019‐nCoV mathematical model. Mathematical Methods in the Applied Sciences.
Banaś, Józef, Mohamed Jleli, Mohammad Mursaleen, Bessem Samet, and Calogero Vetro, eds. Advances in nonlinear analysis via the concept of measure of noncompactness. Singapore: Springer Singapore, 2017.
Nikam, V., Shukla, A. K., & Gopal, D. (2024). Existence of a system of fractional order differential equations via generalized contraction mapping in partially ordered Banach space. International Journal of Dynamics and Control, 12(1), 125-135.
Sumalai, P., Nikam, V., Shukla, A. K., Gopal, D., & Khaofong, C. (2024). Solution of system of delay differential equations via new darbo type fixed point theorem in partially ordered banach space. Computational and Applied Mathematics, 43(5), 273.
Schauder, J. (1930). Der fixpunktsatz in funktionalraümen. Studia Mathematica, 2(1), 171-180.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 International Journal of Scientific Research in Science and Technology
This work is licensed under a Creative Commons Attribution 4.0 International License.
