Yazar "Kashuri, Artion" seçeneğine göre listele

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    Fractional integral inequalities for generalized convexity
    (Tbilisi Centre Math Sci, 2020) Kashuri, Artion; Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Hiiseyin; Sarıkaya, Mehmet Zeki
    In this paper, we define a new class of functions called generalized phi-convex function. Several variants of Hermite-Hadamard type fractional integral inequalities are presented. This ideas and techniques used in this paper may open new avenues of research and motivate the reader to explore the application of generalized phi-convex functions in various branches of pure and applied sciences.
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    Fractional Ostrowski Type Inequalities for Interval Valued Functions
    (Univ Nis, Fac Sci Math, 2022) Budak, Hüseyin; Kashuri, Artion; Butt, Saad Ihsan
    In this paper, we establish some generalization of Ostrowski type inequalities for interval valued functions by using the definitions of the gH-derivatives. At the end, a briefly conclusion is given as well.
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    Further refinements and inequalities of Fejer's type via GA-convexity
    (Ramazan Yaman, 2024) Latif, Muhammad Amer; Budak, Hüseyin; Kashuri, Artion
    In this study, we introduce some new mappings in connection with HermiteHadamard and Fejer type integral inequalities which have been proved using the GA-convex functions. As a consequence, we obtain certain new inequalities of the Fejer type that provide refinements of the Hermite-Hadamard and Fejer type integral inequalities that have already been obtained.
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    Generalizations of fractional Hermite-Hadamard-Mercer like inequalities for convex functions
    (Amer Inst Mathematical Sciences-Aims, 2021) Vivas-Cortez, Miguel; Ali, Muhammad Aamir; Kashuri, Artion; Budak, Hüseyin
    In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. We discuss special cases of our main results and give new inequalities of HH and HHM type for different fractional integrals like, Riemann-Liouville (RL) fractional integrals, k-Riemann-Liouville (k-RL) fractional integrals, conformable fractional integrals and fractional integrals of exponential kernel.
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    Generalized fractional integral inequalities of Hermite-Hadamard type for harmonically convex functions
    (Springeropen, 2020) Zhao, Dafang; Ali, Muhammad Aamir; Kashuri, Artion; Budak, Hüseyin
    In this paper, we establish inequalities of Hermite-Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (Iscan in Hacet. J. Math. Stat. 43(6):935-942, 2014 and Iscan and Wu in Appl. Math. Comput. 238:237-244, 2014). We also discuss some special cases for our main results and obtain new inequalities of Hermite-Hadamard type.
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    Hermite-Hadamard type inequalities for F-convex functions involving generalized fractional integrals
    (Babes-Bolyai University, 2022) Budak, Hüseyin; Ali, Muhammad Aamir; Kashuri, Artion
    In this paper, we firstly summarize some properties of the family ? and F-convex functions which are defined by B. Samet. Utilizing generalized fractional integrals new Hermite-Hadamard type inequalities for F-convex functions have been provided. Some results given earlier works are also as special cases of our results. © 2022, Studia Universitatis Babes-Bolyai Mathematica. All rights reserved.
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    Hermite-Hadamard Type Inequalities For The Interval-Valued Harmonically h-Convex Functions Via Fractional Integrals
    (Tsing Hua Univ, Dept Mathematics, 2021) Budak, Hüseyin; Bilisik, Condon Can; Kashuri, Artion; Ali, Muhammad Aamir
    In this paper, we first present a new definition of convex interval-valued functions which is called as interval-valued harmonically h-convex functions. Then, we establish some new Hermite-Hadamard type inequalities for interval-valued harmonically h-convex functions by using fractional integrals. We also discussed some special cases of our main results. Finally, a briefly conclusion is given.
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    Hermite-Hadamard type inequalities for the interval-valued harmonically h-convex functions via fractional integrals
    (Tsing Hua University, 2021) Budak, Hüseyin; Bilişik, Özge Nalan; Kashuri, Artion; Ali, Muhammad Aamir
    In this paper, we first present a new definition of convex interval-valued functions which is called as interval-valued harmonically h-convex functions. Then, we establish some new Hermite-Hadamard type inequalities for interval-valued harmonically h-convex functions by using fractional integrals. We also discussed some special cases of our main results. Finally, a briefly conclusion is given. © 2021, Tsing Hua University. All rights reserved.
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    Hermite-Hadamard-type inequalities for the interval-valued approximatelyh-convex functions via generalized fractional integrals
    (Springer, 2020) Zhao, Dafang; Ali, Muhammad Aamir; Kashuri, Artion; Budak, Hüseyin; Sarıkaya, Mehmet Zeki
    In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called interval-valued approximatelyh-convex functions. We establish some inequalities of Hermite-Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302,2018and H. Budak et al. in Proc. Am. Math. Soc.,2019). We also discussed some special cases from our main results.
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    New estimates of Gauss-Jacobi and trapezium type inequalities for strongly (h(1), h(2))-preinvex mappings via general fractional integrals
    (Semnan Univ, 2021) Kashuri, Artion; Liko, Rozana; Ali, Muhammad Aamir; Budak, Hüseyin
    In this paper, authors discover two interesting identities regarding Gauss-Jacobi and trapezium type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss-Jacobi type integral inequalities for a new class of functions called strongly (h(1), h(2))-preinvex of order sigma> 0 with modulus mu > 0 via general fractional integrals are established. Also, using the second lemma, some new estimates with respect to trapezium type integral inequalities for strongly (h(1), h(2))-preinvex functions of order mu> 0 with modulus mu > 0 via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different real numbers and new approximation error estimates for the trapezoidal are provided as well. These results give us the generalizations of some previous known results. The ideas and techniques of this paper may stimulate further research in the fascinating field of inequalities.
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    On generalized fractional inequalities for functions of bounded variation with two variables
    (Semnan Univ, 2022) Budak, Hüseyin; Özçelik, Kubilay; Kashuri, Artion; Ali, Muhammad Aamir; Zhang, Zhiyue
    In this paper, we firstly obtain some identities via generalized fractional integrals which generalize some important fractional integrals such as the Riemann-Liouville fractional integrals, the Hadamard fractional integrals, etc. Then by utilizing these equalities we establish some Ostrowski and Trapezoid type inequalities for functions of bounded variation with two variables. Moreover, we give some inequalities involving Hadamard fractional integrals as special cases of our main results.
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    ON WEIGHTED GENERALIZATION OF OPIAL TYPE INEQUALITIES IN TWO VARIABLES
    (Kangwon-Kyungki Mathematical Soc, 2020) Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Kashuri, Artion
    In this paper, we establish some weighted generalization of Opial type inequalities in two independent variables for two functions. We also obtain weighted Opial type inequalities by using p-norms. Special cases of our results reduce to the inequalities in earlier study.
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    Ostrowski type inequalities for functions of two variables via generalized fractional integrals
    (Univ Miskolc Inst Math, 2023) Ozcelik, Kubilay; Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Kashuri, Artion
    In this paper, we establish some Ostrowski type integral inequalities for functions of two variables involving generalized fractional integrals. The results presented here provide extensions of those given in earlier works.
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    Parameterized Inequalities of Different Types for Preinvex Functions with Respect to another Function via Generalized Fractional Integral Operators and their Applications
    (Springer, 2022) Kashuri, Artion; Sarıkaya, Mehmet Zeki
    We prove an identity with two parameters for a function differentiable with respect to another function via generalized integral operator. By applying the established identity, we discover the generalized trapezium, midpoint, and Simpson-type integral inequalities. It is indicated that the results of the present research provide integral inequalities for almost all fractional integrals discovered in recent decades. Various special cases are identified. Some applications of the presented results to special means and new error estimates for the trapezium and midpoint quadrature formulas are analyzed. The ideas and techniques of the present paper may stimulate further research in the field of integral inequalities.