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Sahand Communications in Mathematical Analysis، جلد ۲۰، شماره ۴، صفحات ۱-۲۰
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عنوان انگلیسی Fractional Ostrowski-type Inequalities via $(alpha,beta,gamma,delta)-$convex Function
چکیده انگلیسی مقاله In this paper, we are introducing for the first time a generalized class named the class of $(alpha,beta,gamma,delta)-$convex functions of mixed kind. This generalized class contains many subclasses including the class of $(alpha,beta)-$convex functions of the first and second kind, $(s,r)-$convex functions of mixed kind, $s-$convex functions of the first and second kind, $P-$convex functions, quasi-convex functions and the class of ordinary convex functions. In addition, we would like to state the generalization of the classical Ostrowski inequality via fractional integrals, which is obtained for functions whose first derivative in absolute values is $(alpha,beta,gamma,delta)-$ convex function of mixed kind. Moreover, we establish some Ostrowski-type inequalities via fractional integrals and their particular cases for the class of functions whose absolute values at certain powers of derivatives are $(alpha,beta,gamma,delta)-$ convex functions of mixed kind using different techniques including H"older's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, the applications of special means will also be discussed.
کلیدواژه‌های انگلیسی مقاله Ostrowski inequality, Convex functions, Power mean inequality, Hölder&apos,s inequality
نویسندگان مقاله Ali Hassan |
Department of Mathematics, Shah Abdul Latif University Khairpur-66020, Pakistan.

Asif R. Khan |
Department of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan.

Nazia Irshad |
Department of Basic Sciences, Mathematics and Humanities, Dawood University of Engineering and Technology, M. A Jinnah Road, Karachi-74800, Pakistan.

Sumbul Khatoon |
Department of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan.

نشانی اینترنتی https://scma.maragheh.ac.ir/article_704653_02efa3035f17bdc4a68255bcce4caaf5.pdf
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