Yazar "Budak, Hueseyin" seçeneğine göre listele

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    Advances in Ostrowski-Mercer Like Inequalities within Fractal Space
    (Mdpi, 2023) Vivas-Cortez, Miguel; Awan, Muhammad Uzair; Asif, Usama; Javed, Muhammad Zakria; Budak, Hueseyin
    The main idea of the current investigation is to explore some new aspects of Ostrowski's type integral inequalities implementing the generalized Jensen-Mercer inequality established for generalized s-convexity in fractal space. To proceed further with this task, we construct a new generalized integral equality for first-order local differentiable functions, which will serve as an auxiliary result to restore some new bounds for Ostrowski inequality. We establish our desired results by employing the equality, some renowned generalized integral inequalities like Holder's, power mean, Yang-Holder's, bounded characteristics of the functions and considering generalized s-convexity characteristics of functions. Also, in support of our main findings, we deliver specific applications to means, and numerical integration and graphical visualization are also presented here.
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    Bounds for the Error in Approximating a Fractional Integral by Simpson's Rule
    (Mdpi, 2023) Budak, Hueseyin; Hezenci, Fatih; Kara, Hasan; Sarıkaya, Mehmet Zeki
    Simpson's rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann-Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson's inequalities is the first paper in the literature as a method.
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    Bullen-type inequalities for twice-differentiable functions by using conformable fractional integrals
    (Springer, 2024) Hezenci, Fatih; Budak, Hueseyin
    In this paper, we prove an equality for twice-differentiable convex functions involving the conformable fractional integrals. Moreover, several Bullen-type inequalities are established for twice-differentiable functions. More precisely, conformable fractional integrals are used to derive such inequalities. Furthermore, sundry significant inequalities are obtained by taking advantage of the convexity, Holder inequality, and power-mean inequality. Finally, we provide our results by using special cases of obtained theorems.
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    Conformable fractional Newton-type inequalities with respect to differentiable convex functions
    (Springer, 2023) uenal, Cihan; Hezenci, Fatih; Budak, Hueseyin
    The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Holder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation.
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    Exploring Quantum Simpson-Type Inequalities for Convex Functions: A Novel Investigation
    (Mdpi, 2023) Iftikhar, Sabah; Awan, Muhammad Uzair; Budak, Hueseyin
    This study seeks to derive novel quantum variations of Simpson's inequality by primarily utilizing the convexity characteristics of functions. Additionally, the study examines the credibility of the obtained results through the presentation of relevant numerical examples and graphs.
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    Fractional Simpson-Type Inequalities for Twice Differentiable Functions
    (Univ Maragheh, 2023) Budak, Hueseyin; Kara, Hasan; Hezenci, Fatih
    In the literature, several papers are devoted to inequal-ities of Simpson-type in the case of differentiable convex functions and fractional versions. Moreover, some papers are focused on in-equalities of Simpson-type for twice differentiable convex functions. In this research article, we obtain an identity for twice differentiable convex functions. Then, we prove several fractional inequalities of Simpson-type for convex functions.
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    Generalization of quantum calculus and corresponding Hermite-Hadamard inequalities
    (Springer Basel Ag, 2024) Akbar, Saira Bano; Abbas, Mujahid; Budak, Hueseyin
    The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called (phi-h) integrals and (phi-h) derivatives, respectively. Then we investigate some implicit integral inequalities for (phi-h) integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite-Hadamard-type inequalities for q-integrals are deduced. The results presented herein are applicable to convex, m-convex, and & hstrok;-convex functions defined on the non-negative part of the real line.
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    Generalized Hermite-Hadamard inclusions for a generalized fractional integral
    (Rocky Mt Math Consortium, 2023) Budak, Hueseyin; Kara, Hasan; Hezenci, Fatih
    We introduce new generalized fractional integrals for interval-valued functions. Then we prove generalized Hermite-Hadamard type inclusions for interval-valued convex functions using these newly defined generalized fractional integrals. We also show that these results generalize several results obtained in earlier works.
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    The Multi-Parameter Fractal-Fractional Inequalities For Fractal (P,M)-Convex Functions
    (World Scientific Publ Co Pte Ltd, 2024) Yuan, Xiaoman; Budak, Hueseyin; Du, Tingsong
    Local fractional calculus theory and parameterized method have greatly assisted in the advancement of the field of inequalities. To continue its enrichment, this study investigates the multi-parameter fractal-fractional integral inequalities containing the fractal (P,m)-convex functions. Initially, we formulate the new conception of the fractal (P,m)-convex functions and work on a variety of properties. Through the assistance of the fractal-fractional integrals, the 2l-fractal identity with multiple parameters is established, and from that, integral inequalities are inferred regarding twice fractal differentiable functions which are fractal (P,m)-convex. Furthermore, a few typical and novel outcomes are discussed and visualized for specific parameter values, separately. It concludes with some applications in respect of the special means, the quadrature formulas and random variable moments, respectively.
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    New Quantum Hermite-Hadamard-Type Inequalities for p-Convex Functions Involving Recently Defined Quantum Integrals
    (Springer, 2024) Gulshan, Ghazala; Budak, Hueseyin; Hussain, Rashida; Ali, Muhammad Aamir
    We develop new Hermite-Hadamard-type integral inequalities for p-convex functions in the context of q-calculus by using the concept of recently defined T-q-integrals. Then the obtained Hermite-Hadamard inequality for p-convex functions is used to get a new Hermite-Hadamard inequality for coordinated p-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the proposed ideas and techniques may stimulate further research in this field.
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    New Versions of Midpoint Inequalities Based on Extended Riemann-Liouville Fractional Integrals
    (Mdpi, 2023) Hyder, Abd-Allah; Budak, Hueseyin; Barakat, Mohamed A.
    This study aims to prove some midpoint-type inequalities for fractional extended Riemann-Liouville integrals. Crucial equality is proven to build new results. Using this equality, several midpoint-type inequalities are established via differentiable convex functions and the proposed extended fractional operators. To be more specific, the well-known Holder, Jensen, and power mean integral inequalities are employed in the demonstrated inequalities. Additionally, many remarks based on specific selections of the main results are presented. Moreover, to illustrate the key conclusions, a few instances are provided.
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    On Fractional Ostrowski-Mercer-Type Inequalities and Applications
    (Mdpi, 2023) Ramzan, Sofia; Awan, Muhammad Uzair; Vivas-Cortez, Miguel; Budak, Hueseyin
    The objective of this research is to study in detail the fractional variants of Ostrowski-Mercer-type inequalities, specifically for the first and second order differentiable s-convex mappings of the second sense. To obtain the main outcomes of the paper, we leverage the use of conformable fractional integral operators. We also check the numerical validations of the main results. Our findings are also validated through visual representations. Furthermore, we provide a detailed discussion on applications of the obtained results related to special means, q-digamma mappings, and modified Bessel mappings.
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    On Hermite-Hadamard-Fejer-Type Inequalities for ?-Convex Functions via Quantum Calculus
    (Mdpi, 2023) Arunrat, Nuttapong; Nonlaopon, Kamsing; Budak, Hueseyin
    In this paper, we use qa- and qb-integrals to establish some quantum Hermite-Hadamard-Fejer-type inequalities for ?-convex functions. By taking q & RARR;1, our results reduce to classical results on Hermite-Hadamard-Fejer-type inequalities for ?-convex functions. Moreover, we give some examples for quantum Hermite-Hadamard-Fejer-type inequalities for ?-convex functions. Some results presented here for ?-convex functions provide extensions of others given in earlier works for convex and ?-convex functions.
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    Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables
    (Springer, 2021) Ali, Muhammad Aamir; Chu, Yu-Ming; Budak, Hueseyin; Akkurt, Abdullah; Yildirim, Hueseyin; Zahid, Manzoor Ahmed
    In this investigation, we demonstrate the quantum version of Montgomery identity for the functions of two variables. Then we use the result to derive some new Ostrowski-type inequalities for the functions of two variables via quantum integrals. We also consider the particular cases of the key results and offer some new integral inequalities.
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    Some Bullen-Type Inequalities For Generalized Fractional Integrals
    (World Scientific Publ Co Pte Ltd, 2023) Zhao, Dafang; Ali, Muhammad Aamir; Budak, Hueseyin; He, Zai-yin
    In this paper, we establish some new Bullen-type inequalities for differentiable convex functions using the generalized fractional integrals. The main advantage of the inequalities and operators used to obtain them is that these inequalities can be turned into some existing inequalities for Riemann integrals and new inequalities for Riemann-Liouville fractional integral inequalities and k-fractional integrals. Finally, we add some applications of special means of real numbers using the newly established inequalities to make these results more interesting.
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    Some remarks on parameterized inequalities involving conformable fractional operators
    (Tubitak Scientific & Technological Research Council Turkey, 2023) Unal, Cihan; Hezenci, Fatih; Budak, Hueseyin
    In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using conformable fractional integrals. To be more precise, parameterized inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Furthermore, previous and new results are presented by using special cases of the obtained theorems.
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    Some Riemann-Liouville fractional integral inequalities of corrected Euler-Maclaurin-type
    (Springernature, 2024) Hezenci, Fatih; Budak, Hueseyin
    In this research article, an equality is established for Riemann-Liouville fractional integral. With the help of this equality, some corrected Euler-Maclaurin-type inequalities are established for the case of differentiable convex functions by using to the well-known Riemann-Liouville fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Moreover, we give example using graph in order to show that our main results are correct. Furthermore, we provide our results by using special cases of obtained theorems.
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    A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators
    (Hindawi Ltd, 2023) Kara, Hasan; Budak, Hueseyin; Etemad, Sina; Rezapour, Shahram; Ahmad, Hijaz; Kaabar, Mohammed K. A.
    This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Holder's inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained.