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      Some new estimates for exponentially $(\hbar,\mathfrak{m})$-convex functions via extended generalized fractional integral operators

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      https://www.riss.kr/link?id=A106482626

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      다국어 초록 (Multilingual Abstract)

      In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fej\'{e}r type inequalities for the exponentially $(\hbar,\mathfrak{m})$-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants ...

      In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fej\'{e}r type inequalities for the exponentially $(\hbar,\mathfrak{m})$-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.

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      참고문헌 (Reference)

      1 A. A. Kilbas, "Theory and applications of frac-tional dierential equations 204" North-Holland Mathematics Studies 2006

      2 G. Rahman, "The extended Mittag-Leer function via fractional calculus" 10 (10): 4244-4253, 2017

      3 S. N. Bernstein, "Sur les fonctions absolument monotones" 52 : 1-66, 1929

      4 M. A. Noor, "Strongly exponentially convex functions" 81/82 : 2019

      5 M. A. Noor, "Some proerties of exponentially preinvex functions" 34 (34): 2019

      6 S. Rashid, "Some new generalizations for exponentially s-convex functions and inequalities via fractional operators" 24 (24): 2019

      7 M. U. Awan, "Some new bounds for Simpson's rule involving special functions via harmonic h-convexity" 10 (10): 1755-1766, 2017

      8 S. S. Dragomir, "Some inequalities for m-convex functions" 38 (38): 21-28, 1993

      9 G. Cristescu, "Some inequalities for functions having Orlicz-convexity" 273 : 226-236, 2016

      10 S. Rashid, "Some generalize Riemann-Liouville frac-tional estimates involving functions having exponentially convexity property" 51 (51): 01-15, 2019

      1 A. A. Kilbas, "Theory and applications of frac-tional dierential equations 204" North-Holland Mathematics Studies 2006

      2 G. Rahman, "The extended Mittag-Leer function via fractional calculus" 10 (10): 4244-4253, 2017

      3 S. N. Bernstein, "Sur les fonctions absolument monotones" 52 : 1-66, 1929

      4 M. A. Noor, "Strongly exponentially convex functions" 81/82 : 2019

      5 M. A. Noor, "Some proerties of exponentially preinvex functions" 34 (34): 2019

      6 S. Rashid, "Some new generalizations for exponentially s-convex functions and inequalities via fractional operators" 24 (24): 2019

      7 M. U. Awan, "Some new bounds for Simpson's rule involving special functions via harmonic h-convexity" 10 (10): 1755-1766, 2017

      8 S. S. Dragomir, "Some inequalities for m-convex functions" 38 (38): 21-28, 1993

      9 G. Cristescu, "Some inequalities for functions having Orlicz-convexity" 273 : 226-236, 2016

      10 S. Rashid, "Some generalize Riemann-Liouville frac-tional estimates involving functions having exponentially convexity property" 51 (51): 01-15, 2019

      11 Gh. Toader, "Some generalizations of the convexity" Univ. Cluj-Napoca 329-338, 1985

      12 S. Rashid, "Some estimates for gener-alized Riemann-Liouville fractional integrals of exponentially convex functions and their applications" 807 (807): 2019

      13 Muhammad Noor, "Some New Classes of Preinvex Functions and Inequalities" MDPI AG 7 (7): 29-, 2019

      14 S. S. Dragomir, "Some Hermite-Hadamard type inequalities for functions whose exponentials are convex" 60 (60): 527-534, 2015

      15 Saima Rashid, "Simpson’s type integral inequalities for ĸ-fractional integrals and their applications" American Institute of Mathematical Sciences (AIMS) 4 (4): 1087-1100, 2019

      16 S. S. Dragomir, "On some new inequalities of Hermite-Hadamard type for m-convex functions" 33 (33): 55-65, 2002

      17 M. E. Ozdemir, "On some inequalities of Hermite-Hadamard type via m-convexity" 23 (23): 1065-1070, 2010

      18 S. Varosanec, "On h-convexity" 326 (326): 303-311, 2007

      19 M. A. Noor, "On exponentially r-convex functions and inequalities" 2019

      20 G. Alirezaei, "On exponentially concave functions and their impact in information theory" 9 (9): 265-274, 2018

      21 S. Pal, "On exponentially concave functions and a new in-formation geometry" 46 (46): 1070-1113, 2018

      22 L. N. Mishra, "On existence and behavior of solutions to some nonlinear inte-gral equations with applications" National Institute of Technology 2017

      23 Dongming Nie, "On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications" MDPI AG 7 (7): 727-, 2019

      24 M. R. Delavar, "On -convexity" 20 (20): 203-216, 2017

      25 Saima Rashid, "New Estimates for Exponentially Convex Functions via Conformable Fractional Operator" MDPI AG 3 (3): 19-, 2019

      26 S. Rashid, "Modied exponential convex functions and inequalities" 2 (2): 45-51, 2019

      27 A. A. Kilbas, "Integral transform with the extended generalized Mittag-Leer function" 11 (11): 173-186, 2006

      28 S. Rashid, "Integral inequalities for gen-eralized preinvex functions" 51 (51): 77-91, 2019

      29 Saima Rashid, "Inequalities Pertaining Fractional Approach through Exponentially Convex Functions" MDPI AG 3 (3): 37-, 2019

      30 I. Iscan, "Hermite-Hadamard-Fejer type inequalities for convex functions via frac-tional integrals" 60 (60): 355-366, 2015

      31 E. Set, "Hermite-Hadamard's inequality and its extensions for conformable fractional integrals of any order > 0" 27 : 197-206, 2018

      32 M. U. Awan, "Hermite-Hadamard inequalities for exponentially convex functions" 12 (12): 405-409, 2018

      33 M. Tomer, "Hermite Hadamard type Reimann-Liouville fractional integral inequalities for convex funtions" 2016

      34 A. Ur. Rehman, "Generalized convex function and asso-ciated Petrovic's inequality" 17 (17): 122-131, 2019

      35 S. Rashid, "Fractional exponentially m-convex func-tions and inequalities" 17 (17): 464-478, 2019

      36 H. M. Srivastava, "Fractional calculus with an integral opera-tor containing a generalized Mittag-Leer function in the kernel" 211 (211): 198-210, 2009

      37 G. Farid, "Fractional Integral In-equalities of Gruss Type via Generalized Mittag-Leer Function" 17 (17): 548-558, 2019

      38 J. Hadamard, "Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann" 58 : 171-215, 1893

      39 M. A. Latif, "Estimates of Hermite-Hadamard inequality for twice dierentiable harmonically-convex functions with applications" 50 (50): 1-13, 2018

      40 R. Vandana, "Duality Relations for a Class of a Multiobjective Fractional Programming Problem Involving Support Functions" Scientific Research Publishing, Inc. 8 : 294-311, 2018

      41 C. P. Niculescu, "Convexity according to means" 6 (6): 571-579, 2003

      42 A. G. Azpeitia, "Convex functions and the Hadamard inequality" 28 (28): 7-12, 1994

      43 T. P. Prabhakar, "A singular integral equation with a generalized Mittag Leer function in the kernel" 19 : 7-15, 1971

      44 T. O. Salim, "A generalization of Mittag-Leer function and integral operator associated with fractional calculus" 3 (3): 1-13, 2012

      45 Deepmala, "A Study on Fixed Point Theorems for Nonlinear Contractions and its Applications" Pt. Ravishankar Shukla University 2014

      46 Lakshmi Narayan Mishra, "$k-$fractional integral inequalities for $(h-m)-$convex functions via Caputo $k-$fractional derivatives" 강원경기수학회 27 (27): 357-374, 2019

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