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Öğe A GENERALIZED AND REFINED PERTURBED VERSION OF OSTROWSKI TYPE INEQUALITIES(Etamaths Publ, 2017) Sarıkaya, Mehmet Zeki; Budak, Hüseyin; Erden, Samet; Qayyum, AtherIn this paper, we first obtain a new identity for twice differentiable mappings. Then, we establish generalized and improved perturbed version of Ostrowski type inequalities for functions whose derivatives are of bounded variation or second derivatives are either bounded or Lipschitzian.Öğe AN IMPROVED VERSION OF PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITIES(Univ Prishtines, 2016) Sarıkaya, Mehmet Zeki; Budak, Hüseyin; Qayyum, AtherThe purpose of this paper is to establish an improved version of perturbed companion of Ostrowski type integral inequalities for functions whose first derivatives are either bounded or of bounded variation.Öğe Improvement in Companion of Ostrowski Type Inequalities for Mappings Whose First Derivatives are of Bounded Variation and Applications(Univ Nis, Fac Sci Math, 2017) Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Qayyum, AtherThe main aim of this paper is to obtain a improved and generalized version of companion of Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation. Some previous results are also recaptured as special cases. New quadrature formulae are also provided.Öğe A New extension of Hermite Hadamard inequalities associating ψ-Hilfer fractional integral(Palestine Polytechnic University, 2025) Qayyum, Ather; Budak, H¨Useyin; Bat, Umut; Kara, Hasan; Munir, Arslan; Rathour, LaxmiFractional inequalities have been an essential topic in mathematics and have found applications in various domains. In this article, we established some new bounds (below and above) for mid-point type inequality and trapezoidal-type inequality for ψ-Hilfer- fractional integral by utilizing functions whose second derivatives are bounded. We also investigate some new generalization and extension of Hermite-Hadamard type inequalities for ψ-Hilfer fractional integrals for the functions having the condition: (Formula presented). © 2025 Elsevier B.V., All rights reserved.Öğe Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function(Taylor & Francis Inc, 2024) Munir, Arslan; Vivas-Cortez, Miguel; Qayyum, Ather; Budak, Hüseyin; Faiz, Irza; Supadi, Siti SuzlinFractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for $s$s-convex function are obtained. By employing well-known inequalities such as H & ouml;lder's and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.Öğe Some New Improvements of Hermite-Hadamard Type Inequalities Using Strongly (s, m)-Convex Function with Applications(Univ Maragheh, 2025) Munir, Arslan; Budak, Huseyin; Kashuri, Artion; Faiz, Irza; Kara, Hasan; Qayyum, AtherThe trapezoidal-type inequalities are discovered in this study using the fractional operator, which produces powerful results. We established a general identity for Caputo-Fabrizio integral operators and the second derivative function. Using this identity new error bounds and estimates for strongly (s, m)-convex functions are obtained. Moreover, some novel trapezoidal-type inequalities are offered taking this identity into account using the known inequalities like Young, Jensen, Holder and power-mean inequalities. Finally, we present some applications for matrix inequality, estimation error regarding trapezoidal formulas and special means for real numbers.Öğe A study of Milne-type inequalities for several convex function classes with applications(Univ Nis, Fac Sci Math, 2024) Munir, Arslan; Qayyum, Ather; Budak, Huseyin; Faiz, Irza; Kara, Hasan; Supadi, Siti SuzlinFractional integral operators have indeed been the subject of significant research in various mathematical and scientific disciplines over the past few decades. The main aim of this article is to establish a new identity employing the Atangana Baleanu fractional integral operator for the case of differentiable functions. Moreover, we present several fractional Milne-type inequalities for bounded function by fractional integrals. Furthermore, we obtain fractional Milne-type inequalities for the case of Lipschitzian functions. Lastly, we explore applications related to special means, and quadrature formulas.Öğe A Study of Some New Hermite-Hadamard Inequalities via Specific Convex Functions with Applications(Mdpi, 2024) Junjua, Moin-ud-Din; Qayyum, Ather; Munir, Arslan; Budak, Hüseyin; Saleem, Muhammad Mohsen; Supadi, Siti SuzlinConvexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques. These inequalities have several applications in different fields such as optimization, mathematical modeling and signal processing. The main goal of this article is to establish a novel and generalized identity for the Caputo-Fabrizio fractional operator. With the help of this specific developed identity, we derive new fractional integral inequalities via exponential convex functions. Furthermore, we give an application to some special means.
