NEW GENERALIZATION AND REFINEMENT OF THE DIAMOND-α INTEGRAL CAUCHY–SCHWARTZ INEQUALITY ON TIME SCALES

Huiyu Tang, Guangsheng Chen and Wen Ting Luo
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Huiyu Tang: Department of Teacher Education, Guangxi Modern Polytechnic College, Hechi 547000, P. R. China
Guangsheng Chen: ��College of Mathematics and Computer Science, Guangxi Science & Technology Normal University, Laibin 546199, P. R. China
Wen Ting Luo: ��College of Mathematics and Computer Science, Guangxi Science & Technology Normal University, Laibin 546199, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-9

Abstract: This paper is concerned with new generalizations and refinements of the diamond-α integral Cauchy–Schwartz inequality on time scales. The new generalization and refinement of the Cauchy–Schwartz inequality related to diamond integral on time scales are also considered. These obtained inequalities unify continuous inequalities and their corresponding discrete forms associated with Cauchy–Schwartz inequality.

Keywords: Diamond-α Integral; Cauchy–Schwartz; Inequality; Refinement; Time Scales (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24400541

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