Common fixed point theorems in modular metric spaces with applications to nonlinear integral equation of Urysohn type

Abdou, A.A.N. 2016. Some fixed point theorems in modular metric spaces. Journal of Nonlinear Sciences and Applications 9: 4381–4387. Banach, S. 1922. Sur les operations dans les ensembles abstracts et leure application aux equations integrals. Fundamenta Mathematicae 3: 133–181. Chaipunya, P., Y.J. Cho, and P. Kumam. 2012. Geraghty-type theorems in modular metric spaces with application to partial differential equation. Advances in Difference Equations 83: 1687–1847. Chistyakov, V.V. 2010. Metric Modular spaces, I basic concepts. Nonlinear Analysis: Theory Methods and Applications 72: 1–14. Chistyakov, V.V. 2010. Metric Modular spaces. II Applications to superposition operators. Nonlinear Analysis: Theory Methods and Applications 72: 15–30. Chistyakov, V. V. 2011. A fixed point theorem for contractions in metric Modular spaces. arXiv:1112.5561, 65–92. Dass, B.K., and S. Gupta. 1975. An extension of Banach contraction principle through rational expressions. Indian Journal of Pure and Applied Mathematics 6: 1455–1458. Geraghty, M. 1973. On contractive mapping. Proceedings of the American Mathematical Society 40: 604–608. Jaggi, D.S. 1977. Some unique fixed point theorems. Indian Journal of Pure and Applied Mathematics 8: 223–230. Khamsi, M.A., W.M. Kozlowski, and S. Reich. 1990. Fixed point theory in modular functions spaces. Nonlinear Analysis 14: 935–953. Mongkolkeha, C., W. Sintunavarat, and P. Kumam, 2011. Fixed point theorem for contraction mappings in modular spaces. Fixed Point Theory and Applications 93:9. Okeke, G. A., S. A. Bishop, S. H. Khan. 2018. Iterative approximation of fixed point of multivalued \(\rho\)-quasi-nonexpansive mappings in modular function spaces with applications. Journal of Function Spaces 2018:9. Okeke, G.A., and S.H. Khan. 2020. Approximation of fixed point of multivalued \(\rho\)-quasi-contractive mappings in modular function spaces. Arab Journal of Mathematical Sciences 26 (1/2): 75–93. Okeke, G.A., and J.K. Kim. 2019. Approximation of common fixed point of three multi-valued \(\rho\)-quasi-nonexpansive mappings in modular function spaces. Nonlinear Functional Analysis and Applications 24 (4): 651–664. Okeke, G.A., D. Francis, and M. de la Sen. 2020. Some fixed point theorems for mappings satisfying rational inequality in modular metric spaces with applications. Heliyon 6: e04785. Okeke, G.A., and D. Francis. 2021. Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces. Arab Journal of Mathematical Sciences. https://doi.org/10.1108/AJMS-10-2020-0098. Okeke, G.A., and D. Francis. 2021. Fixed point theorems for asymptotically \(T\)-regular mappings in preordered modular \(G\)-metric spaces applied to solving nonlinear integral equations. The Journal of Analysis. https://doi.org/10.1007/s41478-021-00354-1. Polyanin, A. D., and A. V. Manzhirov. 2008. Handbook of integral equations Taylor and Francis, New York. Schramm, M. 1985. Functions of \(\Phi\)-bounded variation and Riemann-Stieltjes integration. Transactions of the American Mathematical Society 287: 49–63. Sintunavarat, W., and P. Kumam. 2009. Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition. Applied Mathematics Letters 22: 1877–1881. Sintunavarat, W., and P. Kumam. 2012. Common fixed point theorem for hybrid generalized multi-valued contraction mappings. Applied Mathematics Letters 25: 52–57. Sitthikul, K., and S. Saejung. 2012. Some fixed point theorems in complex valued metric spaces. Fixed Point Theory and Applications 189:11.