Table Of ContentTrends in Mathematics
Praveen Agarwal
Silvestru Sever Dragomir
Mohamed Jleli
Bessem Samet
Editors
Advances in
Mathematical
Inequalities and
Applications
Trends in Mathematics
Trends in Mathematics is a series devoted to the publications of volumes arising
fromconferences andlecture series focusing onaparticulartopicfrom anyarea of
mathematics. Its aim is to make current developments available to the community
as rapidly as possible without compromise to quality and to archive these for
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More information about this series at http://www.springer.com/series/4961
Praveen Agarwal Silvestru Sever Dragomir
(cid:129)
Mohamed Jleli Bessem Samet
(cid:129)
Editors
Advances in Mathematical
Inequalities and Applications
Editors
Praveen Agarwal MohamedJleli
Department ofMathematics Department ofMathematics
Anand International Collegeof Engineering KingSaud University
Jaipur,India Riyadh, SaudiArabia
and BessemSamet
Department ofMathematics
International Centrefor Basic KingSaud University
andAppliedSciences Riyadh, SaudiArabia
Jaipur,India
SilvestruSeverDragomir
Department ofMathematics
Victoria University
Melbourne, VIC,Australia
ISSN 2297-0215 ISSN 2297-024X (electronic)
Trends inMathematics
ISBN978-981-13-3012-4 ISBN978-981-13-3013-1 (eBook)
https://doi.org/10.1007/978-981-13-3013-1
LibraryofCongressControlNumber:2018958925
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Contents
Inequalities for the Generalized k-g-Fractional Integrals in Terms
of Double Integral Means. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Silvestru Sever Dragomir
Existence Theory on Modular Metric Spaces. . . . . . . . . . . . . . . . . . . . . 29
Anantachai Padcharoen, Parin Chaipunya and Poom Kumam
Lyapunov Inequalities for Some Differential Equations
with Integral-Type Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . 59
Rui A. C. Ferreira
A New Class of Generalized Convex Functions and Integral
Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Mohamed Jleli, Donal O’Regan and Bessem Samet
Redheffer-Type Inequalities for the Fox–Wright Functions . . . . . . . . . . 91
Khaled Mehrez
Relations of the Extended Voigt Function with Other Families
of Polynomials and Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
M. A. Pathan
Nonlinear Dynamical Model for DNA . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Haci Mehmet Baskonus and Carlo Cattani
A Variety of Nonlinear Retarded Integral Inequalities
of Gronwall Type and Their Applications . . . . . . . . . . . . . . . . . . . . . . . 143
A. A. El-Deeb
On the Integral Inequalities for Riemann–Liouville
and Conformable Fractional Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . 165
M. Emin Ozdemir, Ahmet Ocak Akdemir, Erhan Set and Alper Ekinci
v
vi Contents
Weighted Integral Inequalities in Terms of Omega-Fractional
Integro-Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
P. Agarwal, A. M. Jerbashian and J. E. Restrepo
On Sherman Method to Deriving Inequalities for Some Classes
of Functions Related to Convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Marek Niezgoda
Divisibility of Class Numbers of Quadratic Fields:
Qualitative Aspects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Kalyan Chakraborty, Azizul Hoque and Richa Sharma
Some Identities on Derangement and Degenerate Derangement
Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Taekyun Kim and Dae San Kim
Some Perturbed Ostrowski Type Inequalities for Twice
Differentiable Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Hüseyin Budak, Mehmet Zeki Sarikaya and Silvestru Sever Dragomir
Comprehensive Inequalities and Equations Specified
by the Mittag-Leffler Functions and Fractional Calculus
in the Complex Plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Hüseyin Irmak and Praveen Agarwal
Novel Results on Hermite–Hadamard Kind Inequalities for g-Convex
Functions by Means of (k, r)-Fractional Integral Operators. . . . . . . . . . 311
Eze R. Nwaeze and Delfim F. M. Torres
A Family of Integral Inequalities on the Interval [(cid:1)1;1] . . . . . . . . . . . . 323
Ali Hafidi, Moulay Rchid Sidi Ammi and Praveen Agarwal
A Generalization of Cauchy–Bunyakovsky Integral Inequality
Via Means with Max and Min Values . . . . . . . . . . . . . . . . . . . . . . . . . . 333
P. Agarwal, A. A. Korenovskii and S. M. Sitnik
Editors and Contributors
About the Editors
Praveen Agarwal is a vice principal and full professor of mathematics at the
AnandInternationalCollegeofEngineering,Jaipur,India.Heisalsodirectorofthe
InternationalCentreforBasicandAppliedSciences,India.HeobtainedhisPh.D.in
pure mathematics for his work entitled “Investigation in Generalized Laplace
Transform, Special Functions and Fractional Calculus” from the University of
Rajasthan and Malaviya National Institute of Technology, Jaipur, India, in 2006.
He has written many papers on special functions, fractional calculus, PDE, fixed
point theory, and mathematical physics. He is on the editorial board of various
internationaljournalsandactsasarefereeforanumberofinternationaljournalsin
mathematics.
Silvestru Sever Dragomir isa chair and professor of theory of inequalities at the
School of Engineering and Science, Victoria University, Australia and also a
honorary professor in School of Computational and Applied Mathematics,
University of the Witwatersrand, Johannesburg, South Africa. He is an active
member of the Australian Mathematical Society, the Mathematical Society of
Romania, the Research Group in Mathematical Inequalities and Applications, and
theWorkingGrouponGeneralizedConvexity.Hisresearchareasincludeclassical
mathematical analysis, convex functions, best approximation, numerical integra-
tion, geometry of Banach spaces, operator theory, variational methods, Volterra
integral equations, qualitative theory of differential equations, theory and coding,
guessing theory, adaptive quadrature rules, adaptive cubature rules, numerical
methods for differential equations, numerical methods for PDEs, game theory, and
Kolmogorov complexity.
Mohamed Jleli is a full professor of mathematics at King Saud University, Saudi
Arabia. HeobtainedhisPh.D.inpuremathematicsforhisworkentitled“Constant
meancurvaturehypersurfaces”fromtheFacultyofSciencesofParis12,France,in
2004. He has written several papers on differential geometry, partial differential
vii
viii EditorsandContributors
equations, evolution equations, fractional differential equations, and fixed-point
theory. He is on the editorial boards of various international journals and acts as a
referee for a number of international journals in mathematics.
BessemSamet isafullprofessorofappliedmathematicsatKingSaudUniversity,
Saudi Arabia. He obtained his Ph.D. in applied mathematics for his work entitled
“Topological derivative method for Maxwell equations and its applications” from
Paul Sabatier University, France, in 2004. His research interests include various
branches of nonlinear analysis, such as fixed-point theory, partial differential
equations, differential equations, and fractional calculus. He is the author/coauthor
ofmorethan100paperspublishedinInternationScientificIndexing(ISI)journals.
HewasincludedintheThomsonReuters’listofHighlyCitedResearchersfor2015
and 2016.
List of Contributors
Praveen Agarwal Department of Mathematics, Anand International College of
Engineering, Jaipur, India; International Centre for Basic and Applied Sciences,
Jaipur, India
Ahmet Ocak Akdemir Faculty of Science and Letters, Agri Ibrahim Cecen
University, Agri, Turkey
MoulayRchidSidiAmmi DepartmentofMathematics,AMNEAGroup,Faculty
of Sciences and Techniques, Moulay Ismail University, Errachidia, Morocco
Haci Mehmet Baskonus Department of Computer Engineering, Munzur
University, Tunceli, Turkey
Hüseyin Budak Department of Mathematics, Faculty of Science and Arts, Düzce
University, Düzce, Turkey
Carlo Cattani Engineering School (DEIM), University of Tuscia, Viterbo, Italy
Parin Chaipunya KMUTT-Fixed Point Theory and Applications Research
Group, Theoretical and Computational Science Center (TaCS), King Mongkut’s
University of Technology Thonburi (KMUTT), Thrung Khru, Bangkok, Thailand
Kalyan Chakraborty Harish-Chandra Research Institute, Jhunsi, Allahabad,
India
Silvestru Sever Dragomir Department of Mathematics, College of Engineering
and Science, Victoria University, Melbourne, MC, Australia; DST-NRF Centre of
Excellence in the Mathematical and Statistical Sciences, School of Computer
ScienceandAppliedMathematics,UniversityoftheWitwatersrand,Johannesburg,
South Africa
EditorsandContributors ix
Alper Ekinci Faculty of Science and Letters, Ordu University, Ordu, Turkey
A. A. El-Deeb Department of Mathematics, Faculty of Science, Al-Azhar
University, Nasr, Cairo, Egypt
M. Emin Ozdemir Education Faculty, Uludag University, Bursa, Turkey
Rui A. C. Ferreira Grupo Física-Matemática, Faculdade de Ciências,
UniversidadedeLisboa,Lisboa,Portugal;DepartamentodeCiênciaseTecnologia,
Universidade Aberta, Lisboa, Portugal
Ali Hafidi Department of Mathematics, AMNEA Group, Faculty of Sciences and
Techniques, Moulay Ismail University, Errachidia, Morocco
Azizul Hoque Harish-Chandra Research Institute, Jhunsi, Allahabad, India
Hüseyin Irmak Department of Mathematics, Faculty of Science, Çankırı
Karatekin University, Çankırı, Turkey
A. M. Jerbashian Institute of Mathematics, University of Antioquia, Medellin,
Colombia
Mohamed Jleli Department of Mathematics, College of Science, King Saud
University, Riyadh, Saudi Arabia
Taekyun Kim Department of Mathematics, College of Science Tianjin
Polytechnic University, Tianjin, China; Department of Mathematics, Kwangwoon
University, Seoul, Republic of Korea
DaeSanKim DepartmentofMathematics,SogangUniversity,Seoul,Republicof
Korea
A. A. Korenovskii Department of Mathematical Analysis, Institute of
Mathematics, Economics and Mechanics, Odessa I.I. Mechnikov National
University, Odessa, Ukraine
Poom Kumam KMUTT-Fixed Point Theory and Applications Research Group,
TheoreticalandComputationalScienceCenter(TaCS),KingMongkut’sUniversity
of Technology Thonburi (KMUTT), Thrung Khru, Bangkok, Thailand
Khaled Mehrez Département de Mathématiques ISSAT Kasserine, Université de
Kairouan, Kairouan, Tunisia
Marek Niezgoda Department of Applied Mathematics and Computer Science,
University of Life Sciences in Lublin, Lublin, Poland
EzeR.Nwaeze DepartmentofMathematics,TuskegeeUniversity,Tuskegee,AL,
USA
Donal O’Regan School of Mathematics, Statistics and Applied Mathematics,
National University of Ireland, Galway, Ireland
