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    EARTHQUAKE -FUNCTIONS WITH SOME RELATED INEQUALITIES AND THEIR APPLICATIONS
    (Editura Bibliotheca-Bibliotheca Publ House, 2025) Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye
    As researchers, our primary commitment is to engage in the creation of scientific and academic knowledge. Recognizing the importance of societal impact, we also strive to contribute to social awareness through our work. Natural disasters, such as floods, earthquakes, avalanches, landslides, tsunamis, and others, frequently afflict regions globally, resulting in profound human losses and extensive material damage. Notably, the earthquake that struck our country on February 6, 2023, marked as the disaster of the century, deeply affected eleven provinces, leading to a tragic loss of tens of thousands of lives. In this paper, we investigate the concept of earthquake P-functions. We establish the Hermite-Hadamard inequality for this class of functions and derive several refinements of the Hermite-Hadamard type inequality for functions whose first derivative, in absolute value, at a certain power, is an earthquake P-function. We present some applications of the trapezoidal formula. We also provide new bounds for special means of different non-negative real numbers.
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    GENERALIZED n-POLYNOMIAL P- FUNCTIONS WITH SOME RELATED INEQUALITIES AND THEIR APPLICATIONS
    (Editura Bibliotheca-Bibliotheca Publ House, 2024) Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye
    In this paper, we introduce the notion of generalized n-polynomial Pfunction. We explore some algebraic properties of this function class. Additionally, we establish a new trapezium type inequality for this generalized class of functions and derive several refinements of the trapezium type inequality for functions whose first derivative in absolute value at a certain power is generalized n-polynomial P-function. Finally, we conclude our paper by exploring some applications of the results we have obtained in the context of special means. Our novel findings generalize previously known results in the literature.
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    Generalized strongly n-polynomial convex functions and related inequalities
    (Springer, 2024) Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye
    This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite-Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite-Hadamard type are derived for this class of functions using the Holder-Iscan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided.