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Inequalities

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ISBN: 9783039280629 9783039280636 Year: Pages: 204 DOI: 10.3390/books978-3-03928-063-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Science (General)
Added to DOAB on : 2020-01-30 16:39:46
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Abstract

Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.

Keywords

analytic functions --- starlike functions --- convex functions --- Fekete-Szegö inequality --- Hilbert C*-module --- g-frame --- g-Bessel sequence --- adjointable operator --- analytic functions --- starlike functions --- convex functions --- Fekete-Szegö inequality --- operator inequality --- positive linear map --- operator Kantorovich inequality --- geometrically convex function --- frame --- weaving frame --- weaving frame operator --- alternate dual frame --- Hilbert space --- quantum estimates --- Hermite-Hadamard type inequalities --- quasi-convex --- Hermite–Hadamard type inequality --- strongly ?-convex functions --- Hölder’s inequality --- Power mean inequality --- Katugampola fractional integrals --- Riemann–Liouville fractional integrals --- Hadamard fractional integrals --- Steffensen’s inequality --- higher order convexity --- Green functions --- Montgomery identity --- Fink’s identity --- Hermite-Hadamard inequality --- interval-valued functions --- (h1, h2)-convex --- majorization inequality --- twice differentiable convex functions --- refined inequality --- Taylor theorem --- Gronwall–Bellman inequality --- proportional fractional derivative --- Riemann–Liouville and Caputo proportional fractional initial value problem --- convex functions --- Fejér’s inequality --- special means --- weaving frame --- weaving K-frame --- K-dual --- pseudo-inverse --- ?-variation --- one-sided singular integral --- commutator --- one-sided weighted Morrey space --- one-sided weighted Campanato space --- power inequalities --- exponential inequalities --- trigonometric inequalities --- weight function --- half-discrete Hardy-Hilbert’s inequality --- parameter --- Euler-Maclaurin summation formula --- reverse inequality

Fractional Differential Equations: Theory, Methods and Applications

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ISBN: 9783039217328 9783039217335 Year: Pages: 172 DOI: 10.3390/books978-3-03921-733-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.

Integral Transforms and Operational Calculus

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ISBN: 9783039216185 9783039216192 Year: Pages: 510 DOI: 10.3390/books978-3-03921-619-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Abstract

Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.

Keywords

highly oscillatory --- convolution quadrature rule --- volterra integral equation --- Bessel kernel --- convergence --- higher order Schwarzian derivatives --- Janowski star-like function --- Janowski convex function --- bound on derivatives --- tangent numbers --- tangent polynomials --- Carlitz-type q-tangent numbers --- Carlitz-type q-tangent polynomials --- (p,q)-analogue of tangent numbers and polynomials --- (p,q)-analogue of tangent zeta function --- symmetric identities --- zeros --- Lommel functions --- univalent functions --- starlike functions --- convex functions --- inclusion relationships --- analytic function --- Hankel determinant --- exponential function --- upper bound --- nonlinear boundary value problems --- fractional-order differential equations --- Riemann-Stieltjes functional integral --- Liouville-Caputo fractional derivative --- infinite-point boundary conditions --- advanced and deviated arguments --- existence of at least one solution --- Fredholm integral equation --- Schauder fixed point theorem --- Hölder condition --- generalized Kuramoto–Sivashinsky equation --- modified Kudryashov method --- exact solutions --- Maple graphs --- analytic function --- Hadamard product (convolution) --- partial sum --- Srivastava–Tomovski generalization of Mittag–Leffler function --- subordination --- differential equation --- differential inclusion --- Liouville–Caputo-type fractional derivative --- fractional integral --- existence --- fixed point --- Bernoulli spiral --- Grandi curves --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- orthogonality property --- symmetric --- encryption --- password --- hash --- cryptography --- PBKDF --- q–Bleimann–Butzer–Hahn operators --- (p,q)-integers --- (p,q)-Bernstein operators --- (p,q)-Bleimann–Butzer–Hahn operators --- modulus of continuity --- rate of approximation --- K-functional --- Hurwitz-Lerch zeta function --- generalized functions --- analytic number theory --- ?-generalized Hurwitz-Lerch zeta functions --- derivative properties --- series representation --- basic hypergeometric functions --- generating functions --- q-polynomials --- analytic functions --- Mittag–Leffler functions --- starlike functions --- convex functions --- Hardy space --- vibrating string equation --- initial conditions --- spectral decomposition --- regular solution --- the uniqueness of the solution --- the existence of a solution --- analytic --- ?-convex function --- starlike function --- strongly-starlike function --- subordination --- q -Sheffer–Appell polynomials --- generating relations --- determinant definition --- recurrence relation --- q -Hermite–Bernoulli polynomials --- q -Hermite–Euler polynomials --- q -Hermite–Genocchi polynomials --- Volterra integral equations --- highly oscillatory Bessel kernel --- Hermite interpolation --- direct Hermite collocation method --- piecewise Hermite collocation method --- differential operator --- q-hypergeometric functions --- meromorphic function --- Mittag–Leffler function --- Hadamard product --- differential subordination --- starlike functions --- Bell numbers --- radius estimate --- (p, q)-integers --- Dunkl analogue --- generating functions --- generalization of exponential function --- Szász operator --- modulus of continuity --- function spaces and their duals --- distributions --- tempered distributions --- Schwartz testing function space --- generalized functions --- distribution space --- wavelet transform of generalized functions --- Fourier transform --- analytic function --- subordination --- Dziok–Srivastava operator --- nonlinear boundary value problem --- nonlocal --- multi-point --- multi-strip --- existence --- Ulam stability --- functions of bounded boundary and bounded radius rotations --- subordination --- functions with positive real part --- uniformly starlike and convex functions --- analytic functions --- univalent functions --- starlike and q-starlike functions --- q-derivative (or q-difference) operator --- sufficient conditions --- distortion theorems --- Janowski functions --- analytic number theory --- ?-generalized Hurwitz–Lerch zeta functions --- derivative properties --- recurrence relations --- integral representations --- Mellin transform --- natural transform --- Adomian decomposition method --- Caputo fractional derivative --- generalized mittag-leffler function --- analytic functions --- Hadamard product --- starlike functions --- q-derivative (or q-difference) operator --- Hankel determinant --- q-starlike functions --- fuzzy volterra integro-differential equations --- fuzzy general linear method --- fuzzy differential equations --- generalized Hukuhara differentiability --- spectrum symmetry --- DCT --- MFCC --- audio features --- anuran calls --- analytic functions --- convex functions --- starlike functions --- strongly convex functions --- strongly starlike functions --- uniformly convex functions --- Struve functions --- truncated-exponential polynomials --- monomiality principle --- generating functions --- Apostol-type polynomials and Apostol-type numbers --- Bernoulli, Euler and Genocchi polynomials --- Bernoulli, Euler, and Genocchi numbers --- operational methods --- summation formulas --- symmetric identities --- Euler numbers and polynomials --- q-Euler numbers and polynomials --- Hurwitz-Euler eta function --- multiple Hurwitz-Euler eta function --- higher order q-Euler numbers and polynomials --- (p, q)-Euler numbers and polynomials of higher order --- symmetric identities --- symmetry of the zero

Mathematical Analysis and Applications II

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ISBN: 9783039283842 9783039283859 Year: Pages: 226 DOI: 10.3390/books978-3-03928-385-9 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:09
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Abstract

This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications” . Investigations involving the theory and applications of mathematical analytical tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.

Keywords

common fixed point --- metric-like space --- ?-Geraghty contraction --- triangular ?-admissible mapping --- fixed circle --- common fixed circle --- fixed-circle theorem --- extended partial Sb-metric spaces --- Sb-metric spaces --- fixed point --- generalized hypergeometric functions --- Gauss and confluent hypergeometric functions --- summation theorems of hypergeometric functions --- partial symmetric --- fixed point --- contraction and weak contraction --- Nadler’s theorem --- linear elastostatics --- simple layer potentials --- displacement problem --- existence and uniqueness theorems --- Fredholm alternative --- singular data --- differential equations --- Sheffer polynomial sets --- generating functions --- monomiality principle --- quasi metric space --- Suzuki contractions --- fixed point theorems --- modified ?-distance --- almost perfect functions --- generating function --- series transformation --- gamma function --- Hankel contour --- Fermi–Dirac function --- Bose–Einstein function --- Weyl transform --- series representation --- Hermite–Hadamard inequalities --- (p, q)-derivative --- (p, q)-integral --- convex functions --- fixed point --- Reich contraction --- Hardy–Rogers contraction --- almost b-metric space --- additive (Cauchy) equation --- additive mapping --- Hyers–Ulam stability --- generalized Hyers–Ulam stability --- hyperstability --- bounded index --- bounded L-index in direction --- slice function --- entire function --- bounded l-index --- generalized hypergeometric functions --- classical summation theorems --- generalization --- laplace transforms --- gamma and beta functions --- Szász-Mirakjan operators --- Szász-Mirakjan Beta type operators --- extended Gamma and Beta functions --- confluent hypergeometric function --- Modulus of smoothness --- modulus of continuity --- Lipschitz class --- local approximation --- Voronovskaja type approximation theorem --- operators theory 44A99, 47B99, 47A62 --- special functions 33C52, 33C65, 33C99, 33B10, 33B15 --- Stirling numbers and Touchard polynomials 11B73 --- n/a

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