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4 results on '"Trapezoid inequalities"'

1. A new generalization of some quantum integral inequalities for quantum differentiable convex functions

Author

Yi-Xia Li, Muhammad Aamir Ali, Hüseyin Budak, Mujahid Abbas, and Yu-Ming Chu

Subjects
Hermite–Hadamard inequality, Trapezoid inequalities, Midpoint inequalities, Quantum calculus, Convex functions, Mathematics, QA1-939
Abstract

Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

Published
2021
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2. Certain mean-type fractional integral inequalities via different convexities with applications

Author

Muhammad Samraiz, Fakhra Nawaz, Sajid Iqbal, Thabet Abdeljawad, Gauhar Rahman, and Kottakkaran Sooppy Nisar

Subjects
Mean-type inequalities, h-convex, ( s + 1 ) $(s+1)$ -convex, k-conformable integral, ( k , s ) $(k,s)$ -Riemann–Liouville fractional integral, Conformable integral, Trapezoid inequalities, Mathematics, QA1-939
Abstract

Abstract In this paper, we establish certain generalized fractional integral inequalities of mean and trapezoid type for ( s + 1 ) $(s+1)$ -convex functions involving the ( k , s ) $(k,s)$ -Riemann–Liouville integrals. Moreover, we develop such integral inequalities for h-convex functions involving the k-conformable fractional integrals. The legitimacy of the derived results is demonstrated by plotting graphs. As applications of the derived inequalities, we obtain the classical Hermite–Hadamard and trapezoid inequalities.

Published
2020
Full Text
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3. A new generalization of some quantum integral inequalities for quantum differentiable convex functions

Author

Hüseyin Budak, Yi-Xia Li, Mujahid Abbas, Yu-Ming Chu, Muhammad Ali, and [Belirlenecek]

Subjects
Midpoint inequalities, Inequality, Generalization, media_common.quotation_subject, Mathematics::Classical Analysis and ODEs, Identity (mathematics), Hadamard inequality, QA1-939, Applied mathematics, Differentiable function, Quantum, Mathematics, media_common, Quantum calculus, Algebra and Number Theory, Partial differential equation, Convex functions, Applied Mathematics, Hermite&#8211, Trapezoid inequalities, Hermite–Hadamard inequality, Ordinary differential equation, Hermite-Hadamard Inequalities, Convex function, Analysis
Abstract

In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite-Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite-Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint-trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results. Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [61673169, 11301127, 11701176, 11626101, 11601485, 11971241] The work was supported by the Natural Science Foundation of China (Grant Nos. 61673169, 11301127, 11701176, 11626101, 11601485, 11971241). WOS:000646075900002 2-s2.0-85105001243

Published
2021

4. Certain mean-type fractional integral inequalities via different convexities with applications

Author

Kottakkaran Sooppy Nisar, Fakhra Nawaz, Muhammad Samraiz, Gauhar Rahman, Thabet Abdeljawad, and Sajid Iqbal

Subjects
Pure mathematics, Inequality, Applied Mathematics, media_common.quotation_subject, lcsh:Mathematics, 010102 general mathematics, Conformable integral, Trapezoid inequalities, Type (model theory), ( k , s ) $(k,s)$ -Riemann–Liouville fractional integral, lcsh:QA1-939, 01 natural sciences, k-conformable integral, 010101 applied mathematics, h-convex, ( s + 1 ) $(s+1)$ -convex, Discrete Mathematics and Combinatorics, Mean-type inequalities, 0101 mathematics, Convex function, Analysis, media_common, Mathematics
Abstract

In this paper, we establish certain generalized fractional integral inequalities of mean and trapezoid type for$(s+1)$(s+1)-convex functions involving the$(k,s)$(k,s)-Riemann–Liouville integrals. Moreover, we develop such integral inequalities forh-convex functions involving thek-conformable fractional integrals. The legitimacy of the derived results is demonstrated by plotting graphs. As applications of the derived inequalities, we obtain the classical Hermite–Hadamard and trapezoid inequalities.

Published
2020

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