Our investigations in this paper revolve around exploring fractional variants of inequalities of Milne type by applying twice differentiable convex mappings. Based on some principles of convexity, H & ouml;lder inequality, and power-mean inequality, novel inequalities are derived. The acquired inequalities are supported by illustrative examples, which are calculated via their proofs. Additionally, graphical representations are to verify the examples visually. Furthermore, this investigation unveils fresh findings within the realm of inequalities.

In this paper, we present a new version of Simpson-type inequalities for differentiable functions defined on a subinterval of the positive real axis. The approach involves a nonnegative integrable weight function and provides an identity that refines the classical Simpson inequality by incorporating the first derivative of the function. A key aspect of this work is the inclusion of the Riemann-Liouville fractional integral, through which we derive specific inequalities that extend the classical framework. In certain cases, our results reduce to the well-known Simpson inequality, demonstrating the generality and flexibility of the method.MSC2020 Classification: 26A09, 26D10, 26D15, 33E20

In this paper, we present a novel estimate of Fejèr-type inequalities for a function ψ : [ϱ , ε ] →ℝ , where ψ is continuous on [ϱ , ε ] and twice differentiable on (ϱ , ε ) , without requiring the convexity of ψ on the interval (ϱ , ε ) .

In this paper, we study the qualitative behavior of the rational recursive sequences x(n+1) = x(n-15)/+/- 1 +/- x(n-3)x(n-7)x(n-11)x(n-15), n is an element of N-0 where the initial conditions are arbitrary real numbers. Also, we give the numerical examples and solutions graphs of some cases of difference equations.

The inequalities of Hermite-Hadamard-Fejer and Hemite-Hadamard are one of the most fundamental inequalities of the concept of convex functions. New inequalities and results are obtained from applying these inequalities to many convex functions. This paper deals with Hermite-Hadamard-Fejer type inequality for the strongly s-η-convex function consisting of strong s-convex and strong η-convex functions. Some new results related to the left-hand side of Hermite-Hadamard-type inequalities are obtained such that the modules of the second derivatives of the functions are strongly s-η-convex.

In this paper, we study the qualitative behavior of the rational recursive sequences $$\begin{aligned} x_{n+1}=\frac{x_{n-17}}{\pm 1\pm x_{n-2}x_{n-5}x_{n-8}x_{n-11}x_{n-14}x_{n-17}}, \quad n \in \mathbb {N}_{0} \end{aligned}$$ where the initial conditions are arbitrary nonzero positive real numbers. Also, we give the numerical examples and solutions graphs of some cases of difference equations.

In this paper, we study the qualitative behavior of the rational recursive sequences $$\begin{aligned} x_{n+1}=\frac{x_{n-17}}{\pm 1\pm x_{n-2}x_{n-5}x_{n-8}x_{n-11}x_{n-14}x_{n-17}}, \quad n \in \mathbb {N}_{0} \end{aligned}$$ where the initial conditions are arbitrary nonzero positive real numbers. Also, we give the numerical examples and solutions graphs of some cases of difference equations.

In this paper, we study the qualitative behavior of the rational recursive sequences x_n+1=x_n-15/± 1± x_n-3x_n-7x_n-11x_n-15, n ∈ℕ_0 where the initial conditions are arbitrary real numbers. Also, we give the numerical examples and solutions graphs of some cases of difference equations.

Bu makalede genelleştirilmiş konveks fonksiyonlardan biri olan s-η-konveks fonksiyonunun güçlendirilmiş hali olan, güçlü s-η-konveks fonksiyonlar kavramı tanıtılmaktadır. Güçlü s-η-konveks fonksiyonlar için Hermite-Hadamard tipi eşitsizlikler elde edilmektedir. Ayrıca bu tür fonksiyonlar yardımıyla türevlenebilir dönüşümler için Hermite-Hadamard-Fejer eşitsizliğinde orta ve sağ terimler arasındaki fark tahmin edilerek, Hermite-Hadamard-Fejer tipi eşitsizlik elde edilir. Bu çalışmada bu eşitsizlik için yeni sonuçlar gösterilmektedir.

In this paper, we study the qualitative behavior of the rational recursive sequences x_n+1=x_n-17/± 1± x_n-2x_n-5x_n-8x_n-11x_n-14x_n-17, n ∈ℕ_0 where the initial conditions are arbitrary nonzero positive real numbers. Also, we give the numerical examples and solutions graphs of some cases of difference equations.

We first establish some Ostrowski type inequalities for mappings whose second derivatives absolute values are convex. Then we give some special cases of these inequalities which provide extensions of those given in earlier works. Finally, some applications of these inequalities for special means are also provided.

In this paper, we establish some new results related to the left-hand of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives are strongly s-convex functions in the second sense.Some previous results are also recaptured as a special case.

In this work, we shall consider higher order nonlinear neutral delay difference equation of the typeDelta(m) [x(n) + p(n) x(n-k)(alpha)] + q(n) x(n-l)(beta) = 0, n = 0, 1, 2, ...where {p(n)} is a sequence of real numbers, {q(n)} is a sequence of nonnegative real numbers, k and l are positive integers and alpha, beta is an element of (0, infinity) are quotient of odd positive integers. We obtain sufficient conditions for the oscillations of all solutions of this equation.

Our aim in this paper is to obtain sufficient conditions for the oscillation of every solution of first order difference equations xn+1 − xn + m ∑ i=1 (pixn−ki − qixn−li) = 0, n = 0, 1, 2, ... and xn+1 − xn + m ∑ i=1 (pixn+ki − qixn+li) = 0, n = 0, 1, 2, ... where pi, qi ∈ R and ki, li ∈ N for i = 1, 2, . . . ,m.