doi: 10.17951/a.2021.75.2.13-29 ANNALES UNIVERSITATIS MARIAE CURIE-SKLODOWSKA LUBLIN – POLONIA VOL. LXXV, NO. 2, 2021 SECTIO A 13–29 MARTIN BOHNER, ASIF R. KHAN, MARIA KHAN, FARAZ MEHMOOD and MUHAMMAD AWAIS SHAIKH Generalized perturbed Ostrowski-type inequalities Abstract. In this paper, we present new perturbed inequalities of Ostrowski- type, for twice differentiable functions with absolutely continuous first deriv- ative and second-order derivative in some L p -space for 1 ≤ p ≤∞. 1. Introduction. In 1938, the Ukrainian mathematician Alexander Markowich Ostrowski (1893–1986) presented a new inequality in [25]. This inequality is now known as Ostrowski’s inequality. Many researchers have written papers about generalizations of Ostrowski’s inequality in the past few decades, including [1, 10, 12, 21, 22]. Ostrowski’s inequality has proved to be a huge and remarkable tool for the enlargement of several branches of mathematics. Inequalities involving integrals, which create bounds in physical quantities, are of great significance in the sense that these kinds of inequalities are not only used in integral approximation theory, operator theory, nonlinear analysis, numerical integration, stochastic analysis, infor- mation theory, statistics, and probability theory, but we may also see their applications in various fields such as biological sciences, engineering, and physics. For some recent contributions to the study of Ostrowski’s inequal- ity to different subject areas, we refer to [2, 4, 5, 13–18, 23, 24, 26]. In this paper, we give some new perturbed inequalities of Ostrowski type for second-order differentiable mappings, which generalise and refine the 2020 Mathematics Subject Classification. Primary 26D10; Secondary 26D20, 26D99. Key words and phrases. Ostrowski’s inequality, perturbed inequality, twice differentiable.