Establishment of Ostrowski-Type Inequalities for Multiplicatively Trigonometric Convex Functions
DOI:
https://doi.org/10.55544/jrasb.5.4.16Keywords:
Hölder's inequality, multiplicatively trigonometric convex functions, Ostrowski inequality, trigonometric convex functions, Bessel functionAbstract
In this study, we present new and refined forms of Ostrowski-type inequalities for multiplicatively trigonometric convex functions. The main objective of this research is to derive generalized versions of the classical Ostrowski inequality that are applicable to this class of functions. This theoretical and analytical study is motivated by the proofs of inequalities for convex functions. In this work, the properties of multiplicatively trigonometric convexity, together with analytical methods, are employed to obtain novel and generalized results. Specifically, under the assumption that the absolute value of the derivative is bounded and satisfies the multiplicatively trigonometric convexity condition, new Ostrowski-type bounds are established. Moreover, by employing Hölder's inequality together with the properties of multiplicatively trigonometric convexity, further refined and generalized forms of these inequalities are derived. In addition, the resulting integral expressions are shown to be expressible in terms of the modified Bessel function of order zero, which enhances the analytical interpretation of the main results and facilitates their use in practical computations. In the final part of this study, we demonstrate the applicability of our results by showing that Ostrowski-type inequalities can also be used to establish new bounds and relationships among special means of real numbers, including arithmetic, geometric, harmonic, logarithmic, P-logarithmic, and identric means. The obtained results may find potential applications in applied mathematics and numerical analysis.
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