A Generalized Darbo-Type Fixed Point Theorem Using Monotonicity in Partially Ordered Banach Spaces with Application to Integral Equation
DOI:
https://doi.org/10.32628/IJSRST2511243Keywords:
Measure of Noncompactness, Darbo Fixed Point TheoremAbstract
In this paper, we establish a generalized Darbo-type fixed point theorem for monotone operators in partially ordered Banach spaces. The theorem extends classical fixed point results by incorporating measures of noncompactness and monotonicity with respect to the order structure. The theorem is successfully applied to demonstrate the existence of solution for integral equation.
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Darbo, G. Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova, 24 (1955), 84–92.
Guo, D., & Lakshmikantham, V. Nonlinear Problems in Abstract Cones, Academic Press, 1988.
Agarwal, R. P., Meehan, M., & O'Regan, D. Fixed Point Theory and Applications, Cambridge University Press, 2001.
Bhaskar, T. G., & Lakshmikantham, V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379–1393.
Altun, I., & Turkoglu, D. (2007). A fixed point theorem for mapping satisfying a general contractive condition of operator type. Journal of Computational Analysis & Applications, 9(1).
Akhmerov, R. R., Kamenskii, M. I., Potapov, A. S., Rodkina, A. E., & Sadovskii, B. N. (1992). Measures of noncompactness and condensing operators (Vol. 55). Birkhäuser.
Atangana, A., & Qureshi, S. (2019). Modeling attractors of chaotic dynamical systems with fractal–fractional operators. Chaos, Solitons & Fractals, 123, 320–337.
Banaś, J. (1980). On measures of noncompactness in Banach spaces. Comment. Math. Univ. Carol., 21(1), 131–143.
Caputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 73–85.
Guo, D., Lakshmikantham, V., & Liu, X. (2013). Nonlinear integral equations in abstract spaces (Vol. 373). Springer.
V. Nikam, AK. Shukla, & D. Gopal, 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 (2024), 125-135
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