Generalized Hermite–Hadamard type inequalities for generalized F-convex function via local fractional integrals
In this paper, we will present the new generalized F-convexity and related integral inequalities on fractal sets Rς (0<ς≤1). These developments allow us to develop new bounds for integral inequalities. We will give new generalized Hermite–Hadamard type inequalities in the fractals sense. In this...
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| Published in: | Chaos, solitons and fractals Vol. 168; p. 113172 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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01.03.2023
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| ISSN: | 0960-0779 |
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| Abstract | In this paper, we will present the new generalized F-convexity and related integral inequalities on fractal sets Rς (0<ς≤1). These developments allow us to develop new bounds for integral inequalities. We will give new generalized Hermite–Hadamard type inequalities in the fractals sense. In this work, we present some new results by employing local fractional calculus for twice differentiable functions along with some new definitions. For the development of these new integral inequalities, we will use generalized Hölder-integral inequality and power mean integral inequality by using local fractional calculus. Moreover, we give some new inequalities for midpoint and trapezoid formula for a new class of local fractional calculus. The results raised in this paper provide significant extensions and generalizations of other related results given in earlier works. |
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| AbstractList | In this paper, we will present the new generalized F-convexity and related integral inequalities on fractal sets Rς (0<ς≤1). These developments allow us to develop new bounds for integral inequalities. We will give new generalized Hermite–Hadamard type inequalities in the fractals sense. In this work, we present some new results by employing local fractional calculus for twice differentiable functions along with some new definitions. For the development of these new integral inequalities, we will use generalized Hölder-integral inequality and power mean integral inequality by using local fractional calculus. Moreover, we give some new inequalities for midpoint and trapezoid formula for a new class of local fractional calculus. The results raised in this paper provide significant extensions and generalizations of other related results given in earlier works. |
| ArticleNumber | 113172 |
| Author | Shaokat, Shahid Razzaq, Arslan Rasheed, Tahir |
| Author_xml | – sequence: 1 givenname: Arslan surname: Razzaq fullname: Razzaq, Arslan email: arslanrazzaq0125@gmail.com – sequence: 2 givenname: Tahir surname: Rasheed fullname: Rasheed, Tahir email: tahirtishna24@gmail.com – sequence: 3 givenname: Shahid surname: Shaokat fullname: Shaokat, Shahid email: shahidshoukat215@gmail.com |
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| Cites_doi | 10.1016/S0252-9602(13)60081-8 10.1287/moor.8.2.231 10.3390/fractalfract6030167 10.2989/16073606.2018.1509242 10.1007/978-3-642-20545-3 10.1016/j.mcm.2011.05.026 10.7153/jmi-2020-14-56 10.1007/BF02567770 10.22436/jnsa.010.11.24 10.1002/mma.7081 10.15446/recolma.v50n2.62207 10.22199/issn.0717-6279-2020-01-0001 10.7153/mia-19-94 10.1016/j.camwa.2009.08.002 10.1016/S0045-7825(01)00241-9 10.1002/mma.6319 |
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