Fractional Ostrowski-type Inequalities via (\alpha,\beta,\gamma,\delta)-convex Function

سال انتشار: 1402
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 99

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شناسه ملی سند علمی:

JR_SCMA-20-4_001

تاریخ نمایه سازی: 9 آبان 1402

چکیده 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.

نویسندگان

Ali Hassan

Department of Mathematics, Shah Abdul Latif University Khairpur-۶۶۰۲۰, Pakistan.

Asif R. Khan

Department of Mathematics, University of Karachi, University Road, Karachi-۷۵۲۷۰, Pakistan.

Nazia Irshad

Department of Basic Sciences, Mathematics and Humanities, Dawood University of Engineering and Technology, M. A Jinnah Road, Karachi-۷۴۸۰۰, Pakistan.

Sumbul Khatoon

Department of Mathematics, University of Karachi, University Road, Karachi-۷۵۲۷۰, Pakistan.

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