Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler function

Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler function

Abstract The authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}...

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Main Authors: George Anastassiou, Artion Kashuri, Rozana Liko
Format: Article
Language:English
Published: SpringerOpen 2019-12-01
Series:Arabian Journal of Mathematics
Subjects:
26A51
26A33
26D07
26D10
26D15
33E12
Online Access:https://doi.org/10.1007/s40065-019-00275-9
id doaj-17debd4fdb954afc930c818e1e17b65d
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spelling doaj-17debd4fdb954afc930c818e1e17b65d2020-12-13T12:19:48ZengSpringerOpenArabian Journal of Mathematics2193-53432193-53512019-12-019223124310.1007/s40065-019-00275-9Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler functionGeorge Anastassiou0Artion Kashuri1Rozana Liko2Department of Mathematical Sciences, University of MemphisDepartment of Mathematics, Faculty of Technical Science, University Ismail QemaliDepartment of Mathematics, Faculty of Technical Science, University Ismail QemaliAbstract The authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler function are presented. It is pointed out that some new special cases can be deduced from main results. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.https://doi.org/10.1007/s40065-019-00275-926A5126A3326D0726D1026D1533E12
collection DOAJ
language English
format Article
sources DOAJ
author George Anastassiou
Artion Kashuri
Rozana Liko
spellingShingle George Anastassiou
Artion Kashuri
Rozana Liko
Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler function
Arabian Journal of Mathematics
26A51
26A33
26D07
26D10
26D15
33E12
author_facet George Anastassiou
Artion Kashuri
Rozana Liko
author_sort George Anastassiou
title Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler function
title_short Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler function
title_full Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler function
title_fullStr Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler function
title_full_unstemmed Fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized Mittag–Leffler function
title_sort fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings via an extended generalized mittag–leffler function
publisher SpringerOpen
series Arabian Journal of Mathematics
issn 2193-5343
2193-5351
publishDate 2019-12-01
description Abstract The authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler function are presented. It is pointed out that some new special cases can be deduced from main results. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.
topic 26A51
26A33
26D07
26D10
26D15
33E12
url https://doi.org/10.1007/s40065-019-00275-9
work_keys_str_mv AT georgeanastassiou fractionalintegralinequalitiesforgeneralizedmathbfmmh1ph2qeta1eta2h1ph2qē1ē2convexmappingsviaanextendedgeneralizedmittaglefflerfunction
AT artionkashuri fractionalintegralinequalitiesforgeneralizedmathbfmmh1ph2qeta1eta2h1ph2qē1ē2convexmappingsviaanextendedgeneralizedmittaglefflerfunction
AT rozanaliko fractionalintegralinequalitiesforgeneralizedmathbfmmh1ph2qeta1eta2h1ph2qē1ē2convexmappingsviaanextendedgeneralizedmittaglefflerfunction
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