Özcan, 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.

İncele

Gülsu, Nagihan kurt; Iscan, Imdat; Kadakal, Mahir; Bekar, Kerim

In this paper, the concept of Hg-convex function is given for the first time in the literature. Some inequalities of Hadamard's type for Hg-convex functions are given. Some algebraic properties of Hg-convex functions and special cases are discussed. In addition, we establish some new integral inequalities for Hg-convex functions by using an integral identity.

İncele

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.

AtıfWoS1·OpenAlex1

İncele