On the existence of solution to a class of nonlinear functional integral equations with two variables

[1] A. Alsaadi, M. Kazemi, and M.M.A. Metwali, On generalization of Petryshyn’s fixed point theorem and its application to the product of n-nonlinear integral equations, AIMS Math. 8 (2023), no. 12, 30562–30573.

[2] R. Arab, M. Rabbani, and R. Mollapourasl, On solution of a nonlinear integral equation with deviating argument based the on fixed point technique, Appl. Comput. Math. 14 (2015), no. 1, 38–49.

[3] A. Babaaghaie and K. Maleknejad, A new approach for numerical solution of two-dimensional nonlinear Fredholm integral equations in the most general kind of kernel, based on Bernstein polynomials and its convergence analysis, J. Comput. Appl. Math. 344 (2018), 482–494.

[4] J. Banas and K. Goebel, Measures of Non-Compactness in Banach Spaces, Marcel Dekker, New York, 1980.

[5] J. Banas and K. Sadarangani, Solutions of some functional-integral equations in Banach algebra, Math. Comput. Modell. 38 (2003), no. 3, 245–250.

[6] A. BenAmar, A. Jeribi, and M. Mnif, Some fixed point theorems and application to biological model, Numer. Funct. Anal. Optim. 29 (2008), no. 1–2, 1–23.

[7] J. Caballero, A.B. Mingarelli, and K. Sadarangani, Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative transfer, Electron. J. Differ. Equa. 2006 (2006), Paper No. 57, 11.

[8] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, 1991.

[9] M.A. Darwish and S.K. Ntouyas, On a quadratic fractional Hammerstein–Volterra integral equation with linear modification of the argument, Nonlinear Anal.: Theory Meth. Appl. 74 (2011), no. 11, 3510–3517.

[10] A. Das, B. Hazarika, and P. Kumam, Some new generalization of Darbo’s fixed point theorem and its application on integral equations, Mathematics 7 (2019), no. 3, 214.

[11] S. Deb, H. Jafari, A. Das, and V. Parvaneh, New fixed point theorems via measure of noncompactness and its application on fractional integral equation involving an operator with iterative relations, J. Inequal. Appl. 2003 (2023), Article number: 106.

[12] A. Deep, Deepmala, and J. Rezaei Roshan, Solvability for generalized nonlinear functional integral equations in Banach spaces with applications, J. Integral Equ. Appl. 33 (2021), no. 1, 19–30.

[13] A. Deep, Deepmala, and M. Rabbani, A numerical method for solvability of some non-linear functional integral equations, Appl. Math. Comput. 402 (2021), 125637.

[14] A. Deep, Deepmala, and R. Ezzati, Application of Petryshyn’s fixed point theorem to solvability for functional integral equations, Appl. Math. Comput. 395 (2021), 125878.

[15] A. Deep, A. Kumar, S. Abbas, and B. Hazarika, An existence result for functional integral equations via Petryshyn’s fixed point theorem, J. Integral Equ. Appl. 34 (2022), no. 2, 165–181.

[16] M. Eshaghi, B. Hayati, M. Kamyar, and H. Khodaei, On stability and nonstability of systems of functional equations, Q. Math. 44 (2021), no. 4, 557–567.

[17] B. Hazarika, H.M. Srivastava, R. Arab, and M. Rabbani, Application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution, Appl. Math. Comput. 360 (2019), 131–146.

[18] S. Hu, M. Khavanin, and W.A.N. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal. 34 (1989), no. 3–4, 261–266.

[19] A. Jeribi, A nonlinear problem arising in growing cell populations, Nonlinear Anal.: Real World Appl. 3 (2002), 85–105.

[20] M. Kazemi and R. Ezzati, Existence of solutions for some nonlinear Volterra integral equations via Petryshyn’s fixed point theorem, Int. J. Nonlinear Anal. Appl. 9 (2018), no. 1, 1—12.

[21] M. Kazemi and M.R. Doostdar, Existence results for some weakly singular integral equations via measures of non-compactness, Int. J. Nonlinear Anal. Appl. 15 (2024), no. 2, 301–308.

[22] M. Kunze, On a special class of nonlinear integral equations, J. Integral Equ. Appl. 7 (1995), no. 3, 329–350.

[23] H.R. Marzban, H.R. Tabrizidooz, and M. Razzaghi, A composite collocation method for the nonlinear mixed Volterra–Fredholm–Hammerstein integral equations, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 3, 1186–1194.

[24] R.D. Nussbaum, The fixed point index and fixed point theorems for k-set contractions, PhD thesis, University of Chicago, 1969.

[25] B.G. Pachpatte, Multidimensional Integral Equations and Inequalities, Vol. 9, Springer Science & Business Media, 2011.

[26] W.V. Petryshyn, Structure of the fixed points sets of k-set-contractions, Arch. Ration. Mech. Anal. 40 (1971), 312–328.

[27] M. Rabbani, A. Deep, and Deepmala, On some generalized non-linear functional integral equations of two variables via measures of noncompactness and numerical method to solve it, Math. Sci. 15 (2021), 317–324.

[28] M. Rabbani and S.H. Kiasoltani, Solving of nonlinear system of Fredholm-Volterra integro-differential equations by using discrete collocation method, J. Math. Comput. Sci. 3 (2011), no. 4, 382–389.

[29] P. Saini, U. Cakan, and A. Deep, ¨ Existence of solutions for 2D nonlinear fractional Volterra integral equations in Banach Space, Rocky Mountain J. Math. 53 (2022), no. 6, 1965–1981.

[30] F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Vol. 20, Springer Science and Business Media, 2012.

[31] K. Wang and Q. Wang, Lagrange collocation method for solving Volterra–Fredholm integral equations, Appl. Math. Comput. 219 (2013), no. 21, 10434–10440.

[32] Y.H. Youssri and R.M. Hafez, Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis, Arab. J. Math. 9 (2020), 471–480.