On New Modifications Governed by Quantum Hahn's Integral Operator Pertaining to Fractional Calculus. (14th July 2020)

• Record Type: Journal Article
• Authors: Rashid, Saima; Khalid, Aasma; Rahman, Gauhar; Nisar, Kottakkaran Sooppy; Chu, Yu-Ming
• Other Names: Ólafsson Gestur Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-07-14
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/8262860
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In the article, we present several generalizations for the generalized Čebyšev type inequality in the frame of quantum fractional Hahn's integral operator by using the quantum shift operator σ Ψ q ς = q ς + 1 − q σ ς ∈ l 1, l 2, σ = l 1 + ω / 1 − q, 0 < q < 1, ω ≥ 0 . As applications, we provide some associated variants to illustrate the efficiency of quantum Hahn's integral operator and compare our obtained results and proposed technique with the previously known results and existing technique. Our ideas and approaches may lead to new directions in fractional quantum calculus theory.