Existence results for some weakly singular integral equations via measures of non-compactness

[1] A. Aghajani, R. Allahyari, and M. Mursaleen, A generalization of Darbo’s theorem with application to the solvability of systems of integral equations, J. Comput. Appl. Math. 260 (2014), 68–77.

[2] J. Banas and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, vol. 60, Marcel Dekker, New York, 1980.

[3] A. Darbo, Punti uniti in transformazioni a codominio non compatto, Rend. Accad. Naz. Linccei. 48 (1970), 195–198.

[4] A. Das, B. Hazarika, and M.M. Mursaleen, Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in ℓp(1 ≤ p < ∞), Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. 113 (2019), no. 1, 31–40.

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

[6] A. Deep and B. Hazarika, An existence result for Hadamard type two dimensional fractional functional integral equations via measure of noncompactness, Chaos Solitons Fractals 147 (2021), 110874.

[7] D. Dhiman, L.N. Mishra, and V.N. Mishra, Solvability of some non-linear functional integral equations via measure of noncompactness, Adv. Stud. Contemp. Math. 32 (2022), no. 2, 157–171.

[8] M. Furi and A. Vignoli, Fixed points for densifying mappings, Rend. Accad. Naz. Lincei. 47 (1969), 465–467.

[9] M. Kazemi, On existence of solutions for some functional integral equations in Banach algebra by fixed point theorem, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 1, 451–466.

[10] M. Kazemi and R. Ezzati, Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness, Appl. Math. Comput. 275 (2016), 165–171.

[11] 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.

[12] K. Kumar, L. Rathour, M.K. Sharma, and V.N. Mishra, Fixed point approximation for Suzuki generalized nonexpansive mapping using B(δ,μ) condition, Appl. Math. 13 (2022), no. 2, 215–227.

[13] K. Kuratowski, Sur les espaces completes, Fund. Math. 15 (1930), 301–309.

[14] C. Kuratowski, Topologie, Volume I, Elsevier, 2014.

[15] K. Maleknejad, K. Nouri, and R. Mollapourasl, Existence of solutions for some nonlinear integral equations, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), no. 6, 2559–2564.

[16] L.N. Mishra and R.P. Agarwal, On existence theorems for some nonlinear functional-integral equations, Dyn. Syst. Appl. 25 (2016), no. 3, 303–320.

[17] R. Mollapourasl and A. Ostadi, On solution of functional integral equation of fractional order, Appl. Math. Comput. 270 (2015), 631–643.

[18] H.K. Nashine and R. Arab, Existence of solutions to nonlinear functional-integral equations via the measure of noncompactness, J. Fixed Point Theory Appl. 20 (2018), no. 2, 66.

[19] H.K. Nashine, R. Arab, R.P. Agarwal, and A.S. Haghighi, Darbo type fixed and coupled fixed point results and its application to integral equation, Period. Math. Hung. 77 (2018), 94–107.

[20] R. Nussbaum, The fixed point index and fixed point theorems for k-set contractions, Doctoral dissertation, University of Chicago, 1969.

[21] I. Ozdemir, U. Cakan, and B. Iihan, On the existence of the solution for some nonlinear Volterra integral equations, Abstr. Appl. Anal. 2013 (2013).

[22] W. V. Petryshyn, Structure of the fixed points sets of k-set-contractions, Arch. Rational Mech. Anal. 40 (1970/1971), 312–328.

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

[24] A.G. Sanatee, L. Rathour, V.N. Mishra, and V. Dewangan, Some fixed point theorems in regular modular metric spaces and application to Caratheodory’s type anti-periodic boundary value problem, J. Anal. 31 (2023), no. 1, 619–632.

[25] P. Shahi, L. Rathour, and V.N. Mishra, Expansive fixed point theorems for tri-simulation functions, J. Engin. Exact Sci. 8 (2022), no. 3, 14303-01e.

[26] N. Sharma, L.N. Mishra, V.N. Mishra, and S. Pandey, Solution of delay differential equation via N^v₁ iteration algorithm, Eur. J. Pure Appl. Math. 13 (2020), no. 5, 1110–1130.

[27] K. Tamilvanan, L.N. Mishra, V.N. Mishra, and K. Loganathan, Fuzzy stability results of additive functional equation in different approaches, Ann. Commun. Math. 3 (2020), no. 3, 208–217.

[28] C. Vetro and F. Vetro, On the existence of at least a solution for functional integral equations via measure of noncompactness, Banach J. Math. Anal. 11 (2017), no. 3, 497–512.