Ostrowski type inequalities via exponentially s-convexity on time scales
We introduce the concept of exponentially s-convexity in the second sense on a time scale interval. We prove among other things that if f : [a, b] → R is an exponentially s-convex function, then 1 b − a Z b a f(t)∆t ≤ f(a) eβ(a, x0)(b − a) 2s (h2(a, b))s + f(b) eβ(b, x0)(b − a) 2s (h2...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
ATNAA
2022-10-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2072524 |
| Summary: | We introduce the concept of exponentially s-convexity in the second sense on a time scale interval. We prove
among other things that if f : [a, b] → R is an exponentially s-convex function, then
1
b − a
Z b
a
f(t)∆t
≤
f(a)
eβ(a, x0)(b − a)
2s
(h2(a, b))s +
f(b)
eβ(b, x0)(b − a)
2s
(h2(b, a))s
,
where β is a positively regressive function. By considering special cases of our time scale, one can derive
loads of interesting new inequalities. The results obtained herein are novel to best of our knowledge and they
complement existing results in the literature.
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| ISSN: | 2587-2648 |