Tosun, Ceyda; Kocayigit, Huseyin; Aydin, Tuba agirman

In this study, a new class of surface curves, namely Yi-Darboux slant helices, is investigated. The conditions under which a surface curve is a iY-Darboux slant helix with respect to the Osculating Darboux (OD), Normal Darboux (ND), and Rectifying Darboux (RD) frames are established, and several characterizations are obtained. In particular, necessary and sufficient conditions are derived in terms of the curvature functions associated with these frames. Furthermore, relationships between iY-Darboux slant helices and classical helices and slant helices are established for special surface curves, including geodesics, asymptotic curves, and lines of curvature. Concrete examples on conical and cylindrical surfaces are also presented to illustrate the theoretical results.

İncele

Alkan, Akin; Kocayígít, Huseyin; Aydin, Tuba Agirman

In this article, the differential equation characterizations for D-i-Darboux slant helices given with the help of three new orthogonal frames are introduced for the curves lying on a surface. These moving frames, obtained based on the Darboux frame, are called Osculating Darboux Frame, Normal Darboux Frame, and Rectifying Darboux Frame, respectively.

AtıfWoS1·OpenAlex1

İncele

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

Kadakal, Huriye; Kadakal, Mahir

In this study, we introduce and study the concept of strongly hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the strongly hyperbolic type convex functions. After that, by using an identity, we get some inequalities for strongly hyperbolic type convex functions. In addition, we compare the results obtained with both Holder, Holder-Iscan inequalities and power-mean, improved power-mean integral inequalities.

AtıfWoS2·OpenAlex2

İncele

Kadakal, Huriye; Kadakal, Mahir

In this study, using both Holder's integral inequality and Holder-Iccan integral inequality, some inequalities of Hermite Hadamard type obtained for multiplicatively preinvex P -functions are given. Afterwards, the result obtained with Holder-Iccan inequality has been shown to be better than that obtained with Holder's integral inequality.

AtıfWoS19

İncele

Erpehlivan, Zeliha; Kocayigit, Hüseyin; Aydin, Tuba Agirman

In this study, we examine timelike helices in R-2(4) and some integral characterizations of these curves in terms of Frenet frame. In addition, we study timelike 2B slant helices in R-2(4) and present the differential equations for vector positions.

İncele

Aydin, Tuba Agirman

In this study, the Bezier curves and surfaces, which have an important place in interactive design applications, are expressed in matrix form using a special matrix that gives the coefficients of the Bernstein base polynomial. The matrix forms of higher order derivatives of the Bezier curves and surfaces are obtained. It is demonstrated by numerical examples that the bidirectional transition between the control points and parametric equations of the Bezier curves and surfaces can be easily achieved using these matrix forms. In addition, it is demonstrated that this type of curve and surface, whose control points are known, its higher order derivatives can be calculated without it's parametric equations. In this study, the Bezier curves and surfaces are presented in a more easily understandable and easy to use format in algebraic form for designers.

AtıfOpenAlex3

İncele

Aydin, Tuba Agirman

In this article, the differential equation of lorentzian spherical timelike curves is obtained in E-1(4). It is seen that the differential equation characterizing Lorentzian spherical timelike curves is equivalent to a linear, third order, differential equation with variable coefficients. It is impossible to solve these equations analytically. In this article, a new numerical technique based on hermite polynomials is presented using the initial conditions for the approximate solution. This method is called the modified hermite matrix-collocation method. With this technique, the solution of the problem is reduced to the solution of an algebraic equation system and the approximate solution is obtained. In addition, the validity and applicability of the technique is explained by a sample application.

AtıfWoS1

İncele