Uysal, G.Dutta, H.2024-09-292024-09-292019978-981139607-62194-1009https://doi.org/10.1007/978-981-13-9608-3_4https://hdl.handle.net/20.500.14619/9638International Conference on Mathematical Modelling, Applied Analysis and Computation, ICMMAAC 2018 -- 6 July 2018 through 8 July 2018 -- Jaipur -- 231359Let ? be a non-empty index set consisting of ? indices and ?0 is allowed to be either accumulation point of ? or infinity. We assume that the function K?, K?: R× R? R, has finite Lebesgue integral value on R for all values of its second variable and for any ? (Formula Presented) ? and satisfies some conditions. The main purpose of this work is to investigate the conditions under which Fatou type pointwise convergence is obtained for the operators in the following setting: (Formula Presented), where Pk,? and ?k, ? are real numbers satisfying certain conditions, at p- ? -Lebesgue point of function f. The obtained results are used for presenting some theorems for the rate of convergences. © Springer Nature Singapore Pte Ltd 2019.eninfo:eu-repo/semantics/closedAccessLipschitz conditionNonlinear integral operatorp- ? -Lebesgue pointRate of convergenceUnified approachConference Object10.1007/978-981-13-9608-3_42-s2.0-8507286593483N/A69272