Explanipedia

New estimates on generalized Hermite–Hadamard–Mercer-type inequalities Open

Çetin Yıldız, Samet Erden, Seth Kermausuor, Daniel Breaz, Luminiţa-Ioana Cotîrlâ · 2025

The concept of a convex function plays a crucial role in fields of mathematical analysis and inequality theory. The importance of convex functions is exemplified by Mercer’s inequality. This inequality, which is derived through the applica…

Simpson Type Estimations for Convex Functions via Quantum Calculus Open

Samet Erden, Alp Necmettin, Iftikhar Sabah · 2024

We first establish a new identity including quantum integrals and quantum numbers via q -differentiable functions. After that, with the help of this equality, a Simpson-type inequality for functions whose quantum derivatives in modulus are…

Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula Open

Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gökkurt Özdemir, Neslihan Uyanık · 2024

In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-side…

New Weighted Inequalities for Functions Whose Higher-Order Partial Derivatives Are Co-Ordinated Convex Open

Samet Erden, Mehmet Zeki Sarıkaya · 2024

The purpose of this study is to establish recent inequalities based on double integrals of mappings whose higher-order partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Also, some special cas…

Sekizinci Sınıf Öğrencilerinin Matematiksel Alan Dilini Kullanmalarına İlişkin Hatalarının Giderilmesinde Dijital Öyküleme Uygulaması Open

Burçin Gökkurt, Samet Erden · 2023

Bu araştırma, sekizinci sınıf öğrencilerinin matematiksel alan dilini kullanmalarına ilişkin hatalarının dijital öykülerle giderilmesini amaçlamaktadır. Araştırma, bir devlet ortaokulunda sekizinci sınıfta öğrenim gören toplam 24 öğrenci i…

Generalized Ostrowski type results for twice differentiable functions on fractal sets Open

Samet Erden · 2023

We first obtain a new auxiliary identity by utilizing twice differentiable functions on α−type sets. Afterwards, two generalized Ostrowski type estimations for mappings whose second local fractional derivatives are bounded are derived, and…

Simpson type integral inequalities for generalized strongly convex functions and applications Open

Samet Erden · 2023

We firstly establish an identity of Simpson type involving local fractional integral. By using the obtained result, some new Simpson type integral inequalities for mappings whose certain powers of the local fractional derivatives in modulu…

A Digital Storytelling Application for Resolving Errors in the Use of Mathematical Field Language by Eighth-Grade Students Open

Burçin Gökkurt, Samet Erden · 2023

Bu araştırma, sekizinci sınıf öğrencilerinin matematiksel alan dilini kullanmalarına ilişkin hatalarının dijital öykülerle giderilmesini amaçlamaktadır. Araştırma, bir devlet ortaokulunda sekizinci sınıfta öğrenim gören toplam 24 öğrenci i…

New bounds for q-midpoint-type inequalities via twice q-differentiable functions on quantum calculus Open

Necmettin Alp, Hüseyin Budak, Samet Erden, Mehmet Zeki Sarıkaya · 2022

Some Perturbed Inequalities of Ostrowski Type for Functions whose n-th Derivatives Are Bounded Open

Samet Erden · 2022

We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are o…

Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas Open

Sabah Iftikhar, Samet Erden, Muhammad Aamir Ali, Jamel Baili, Hijaz Ahmad · 2022

Inequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied …

Some perturbed inequalities of Ostrowski type for twice differentiable functions Open

Samet Erden, Hüseyin Budak, Mehmet Zeki Sarıkaya · 2021

We establish new perturbed Ostrowski type inequalities for functions whose second derivatives are of bounded variation. In addition, we obtain some integral inequalities for absolutely continuous mappings. Finally, some inequalities relate…

On some new midpoint inequalities for the functions of two variables via quantum calculus Open

Xuexiao You, Muhammad Aamir Ali, Samet Erden, Hüseyin Budak, Yu‐Ming Chu · 2021

In this paper, first we obtain a new identity for quantum integrals, the result is then used to prove midpoint type inequalities for differentiable coordinated convex mappings. The outcomes provided in this article are an extension of the …

Some New Simpson’s and Newton’s Formulas Type Inequalities for Convex Functions in Quantum Calculus Open

Pimchana Siricharuanun, Samet Erden, Muhammad Aamir Ali, Hüseyin Budak, Saowaluck Chasreechai , et al. · 2021

In this paper, using the notions of qκ2-quantum integral and qκ2-quantum derivative, we present some new identities that enable us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for quantum differentiable convex fun…

Improved results of perturbed inequalities for higher-order differentiable functions and their various applications Open

Samet Erden, Bahar Başkır · 2021

A new integral equality for the function whose higher order derivatives are absolutely continuous are first improved by using the quadratic kernel mapping with five sections. After that, refined inequalities of perturbed Ostrowski type for…

On Fejér type inclusions for products of interval-valued convex functions Open

Hüseyin Budak, Hasan Kara, Samet Erden · 2021

We first get some new Fej?r type inclusions for products of interval-valued convex mappings. The most important feature of our work is that it contains Fej?r type inclusions for both interval-valued integrals and interval-valued fractional…

Some perturbed inequalities of Ostrowski type for high-order differentiable functions and applications Open

Samet Erden, Mehmet Zeki Sarıkaya · 2020

We firstly establish inequalities for functions whose high degree derivatives are convex via an equality which was presented previously. Then we derive inequalities for functions whose high-order derivatives are absolutely continuous by us…

Some Weighted Inequalities for Higher-Order Partial Derivatives in Two Dimensions and Its Applications Open

Samet Erden, Mehmet Zeki Sarıkaya · 2020

We establish some Ostrowski type inequalities involving higher-order partial derivatives for two-dimensional integrals on Lebesgue spaces (L_{∞}, L_{p} and L₁). Some applications in Numerical Analysis in connection with cubature formula ar…

Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications Open

Samet Erden, Nuri Çelik, Muhammad Adil Khan · 2020

First of all, we establish an identity for higher-order differentiable functions. Then, we prove some integral inequalities for mappings that have continuous derivatives up to the order $n-1$ with $n\geq 1$ and whose n-th derivatives are t…

On Fejér type inclusions for products of interval-valued convex functions Open

Hasan Kara, Hüseyin BUDAK, Samet Erden · 2020

We first get some new Fejér type inclusions for products of interval-valued convex mappings.The most important feature of our work is that it contains Fejér type inclusions for both interval-valued integrals and interval-valued fractional …

Simpson and Newton type inequalities for convex functions via newly defined quantum integrals Open

Hüseyin Budak, Samet Erden, Muhammad Aamir Ali · 2020

We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3…

PERTURBED COMPANIONS OF OSTROWSKI TYPE INEQUALITIES FOR N-TIMES DIFFERENTIABLE FUNCTIONS AND APPLICATIONS Open

Samet Erden · 2020

We firstly examine some inequalities obtained by using sets of complex-valued functions for functions whose high order derivatives are restricted. We also give some approximations for the functions whose derivatives up to the order 𝑛−1 (𝑛 …

Fractional Ostrowski type inequalities for bounded functions Open

Samet Erden, Hüseyin Budak, Mehmet Zeki Sarıkaya, Sabah Iftikhar, Poom Kumam · 2020

ON THE GENERALIZED INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE MAPPINGS Open

Mehmet Zeki Sarıkaya, Samet Erden, Hüseyin Budak · 2020

In this paper, an important integral equality is derived. Then, we establish several new inequalities for some twice differentiable mappings that are connected with the celebrated Hermite-Hadamard type and Ostrowski type integral inequalit…

NEW WEIGHTED OSTROWSKI TYPE INEQUALITIES FOR MAPPINGS WHOSE nTH DERIVATIVES ARE OF BOUNDED VARIATION Open

Hüseyin Budak, Samet Erden, Mehmet Zeki Sarıkaya · 2020

We establish a new generalization of weighted Ostrowski type inequality for mappings of bounded variation. Spacial cases of this inequality reduce some well known inequalities. With the help of obtained inequality, we give applications for…

Local fractional Newton’s inequalities involving generalized harmonic convex functions Open

Sabah Iftikhar, Samet Erden, Poom Kumam, Muhammad Uzair Awan · 2020

Weighted inequalities involving conformable integrals and its applications for random variable and numerical integration Open

Samet Erden · 2020

We establish new weighted inequalities for conformable integrals and derivatives. Then, some results involving ?-fractional moments are presented. Next, ?-fractional Uniform, Gamma and Weibull distribution are defined and exclusive results…

Fractional Ostrowski type inequalities for functions of bounded variaton with two variables Open

Samet Erden, Hüseyin Budak, Mehmet Zeki Sarıkaya · 2020

We first establish some fractional equalities for functions of bounded variation with two variables. Then we derive some fractional Ostrowski and Trapezoid type inequalities for functions of bounded variation with two variables. In additio…

Companions Of Perturbed Type Inequalities For Higher-Order Differentiable Functions Open

Samet Erden · 2019

First of all, a novel inequality of Hadamard's type for functions higher order derivatives of which are convex is developed. It is also presented midpoint type results. Afterward, Ostrowski type inequalities for mappings whose derivatives …

Some inequalities for double integrals and applications for cubature formula Open

Samet Erden, Mehmet Zeki Sarıkaya · 2019

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