Local fractional integrals involving generalized strongly m-convex mappings
In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets R α ( 0 < α ≤ 1 ) of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m...
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| Published in | Arabian Journal of Mathematics Vol. 8; no. 2; pp. 95 - 107 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2019
Springer Springer Nature B.V |
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| Abstract | In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets
R
α
(
0
<
α
≤
1
)
of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly
m
-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results. |
|---|---|
| AbstractList | In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets
R
α
(
0
<
α
≤
1
)
of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly
m
-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results. In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets [R.sup.[alpha]] (0 < [alpha] [less than or equal to] 1) of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results. Mathematics Subject Classification Primary 26A51; Secondary 26A33 * 26D07 * 26D10 * 26D15 [phrase omitted] In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets [R.sup.a] (0 < [alpha] [less than or equal to] 1) of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results. In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets [R.sup.a] (0 < [alpha] [less than or equal to] 1) of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results. Mathematics Subject Classification Primary 26A51; Secondary 26A33 * 26D07 * 26D10 * 26D15 In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets \[{\mathbb {R}}^{\alpha }\, (0<\alpha \le 1)\] of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results. In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets [R.sup.[alpha]] (0 < [alpha] [less than or equal to] 1) of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results. |
| Audience | Academic |
| Author | Anastassiou, George Kashuri, Artion Liko, Rozana |
| Author_xml | – sequence: 1 givenname: George surname: Anastassiou fullname: Anastassiou, George email: ganastss2@gmail.com organization: George Anastassiou Department of Mathematical Sciences, University of Memphis – sequence: 2 givenname: Artion surname: Kashuri fullname: Kashuri, Artion organization: Department of Mathematics, Faculty of Technical Science, University Ismail Qemali – sequence: 3 givenname: Rozana surname: Liko fullname: Liko, Rozana organization: Department of Mathematics, Faculty of Technical Science, University Ismail Qemali |
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| Cites_doi | 10.1007/s40096-017-0227-z 10.22436/jnsa.010.11.32 10.1007/978-3-642-17098-0 10.1016/j.aml.2008.06.003 10.1002/mma.4270 10.1186/s13660-016-1276-9 10.1007/978-0-387-98128-4 10.1007/978-1-4614-0703-4 10.1090/proc/13488 |
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| References | Agarwal (CR1) 2017; 40 Yang (CR25) 2012; 1 Yang, Baleanu, Yang (CR27) 2013; 2013 Mo (CR12) 2014; 2014 Sarikaya, Erden, Budak (CR17) 2015; 18 Anastassiou (CR3) 2009 Set, Tomar (CR19) 2016; 31 Anastassiou (CR4) 2011 Choi, Set, Tomar (CR7) 2017; 32 Sarikaya, Tunç, Budak (CR18) 2016; 276 Yang (CR23) 2011 Yang (CR24) 2012 Sarikaya, Budak (CR16) 2017; 145 Anastassiou (CR5) 2011 Srivastava, Choi (CR20) 2012 Lara, Merentes, Quintero, Rosales (CR10) 2015; 5 Mo, Sui (CR14) 2017; 11 Yang (CR26) 2012; 1 Mo, Sui (CR13) 2014; 2014 Lara, Merentes, Quintero (CR11) 2015; 5 Yang (CR22) 2011; 2011 Budak, Sarikaya, Yildirim (CR6) 2015; 18 Jumarie (CR9) 2009; 22 Erden, Sarikaya (CR8) 2016; 274 Tomar, Agarwal, Jleli, Samet (CR21) 2017; 10 Mo, Sui, Yu (CR15) 2014; 2014 Agarwal, Jleli, Tomar (CR2) 2017; 2017 X-J Yang (214_CR25) 2012; 1 HM Srivastava (214_CR20) 2012 MZ Sarikaya (214_CR17) 2015; 18 H-X Mo (214_CR12) 2014; 2014 E Set (214_CR19) 2016; 31 G Anastassiou (214_CR3) 2009 T Lara (214_CR10) 2015; 5 S Erden (214_CR8) 2016; 274 X-J Yang (214_CR24) 2012 M Tomar (214_CR21) 2017; 10 MZ Sarikaya (214_CR16) 2017; 145 J-S Choi (214_CR7) 2017; 32 G Anastassiou (214_CR4) 2011 G Jumarie (214_CR9) 2009; 22 Y-J Yang (214_CR27) 2013; 2013 H-X Mo (214_CR14) 2017; 11 X-J Yang (214_CR23) 2011 MZ Sarikaya (214_CR18) 2016; 276 X-J Yang (214_CR26) 2012; 1 P Agarwal (214_CR2) 2017; 2017 H-X Mo (214_CR13) 2014; 2014 P Agarwal (214_CR1) 2017; 40 H-X Mo (214_CR15) 2014; 2014 T Lara (214_CR11) 2015; 5 H Budak (214_CR6) 2015; 18 G Anastassiou (214_CR5) 2011 X-J Yang (214_CR22) 2011; 2011 |
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| Snippet | In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets
R
α
(
0
<
α
≤
1
)
of real... In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets [R.sup.a] (0 < [alpha] [less... In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets [R.sup.[alpha]] (0 < [alpha]... In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets \[{\mathbb {R}}^{\alpha }\,... |
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| Title | Local fractional integrals involving generalized strongly m-convex mappings |
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