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    LOGARITHMIC SEMI P-FUNCTION AND SOME NEW INEQUALITIES
    (Erhan SET, 2024) Kadakal, Mahir; İşcan, İmdat
    In this study, we introduce and study the concept of logarithmic semi P functions and their some algebraic properties. Then, we obtain the Hermite-Hadamard integral inequality for the log semi-P-functions. After that, we obtain some new inequalities by using Hölder, Hölder-İşcan and power-mean integral inequalities and show that the result obtained with Hölder-İşcan inequality gives better approach than the Hölder integral inequality. Some applications to special means of real numbers are also given. © 2024, Erhan SET. All rights reserved.
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    Strongly n-polynomial convexity and related inequalities
    (SINUS Association, 2022) Ataman, Canan; Kadakal, Mahir; İşcan, İmdat
    In this paper, we introduce and study the concept of strongly n-polynomial convexity functions and their some algebraic properties. We prove two Hermite-Hadamard type inequalities for the newly introduced class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is strongly n-polynomial convexity. Also, we compare the obtained results with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others. © 2022, SINUS Association. All rights reserved.