New perspectives on the theory of inequalities for integral and sum / / Nazia Irshad [and three others]

• Pubblicazione: Cham, Switzerland : , : Springer International Publishing, , [2022]; ©2022
• Descrizione fisica: 1 online resource (319 pages)
• Disciplina: 515.243
• Soggetto topico: Inequalities (Mathematics); Inequalities (Mathematics) - Data processing; Desigualtats (Matemàtica)
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): IrshadNazia
• Nota di contenuto: Intro -- Preface -- Contents -- Notations and Terminologies -- 1 Linear Inequalities via Interpolation Polynomials and Green Functions -- 1.1 Linear Inequalities and the Extension of Montgomery Identity with New Green Functions -- 1.1.1 Results Obtained by the Extension of Montgomery Identity and New Green Functions -- 1.1.2 Inequalities for n-Convex Functions at a Point -- 1.1.3 Bounds for Remainders and Functionals -- 1.1.4 Mean Value Theorems -- 1.2 Linear Inequalities and the Taylor Formula with New Green Functions -- 1.2.1 Results Obtained by the Taylor Formula and New Green Functions -- 1.2.2 Inequalities for n-Convex Functions at a Point -- 1.2.3 Bounds for Remainders and Functionals -- 1.2.4 Mean Value Theorems and Exponential Convexity -- Mean Value Theorems -- Logarithmically Convex Functions -- n-Exponentially Convex Functions -- 1.2.5 Examples with Applications -- 1.3 Linear Inequalities and Hermite Interpolation with New Green Functions -- 1.3.1 Results Obtained by the Hermite Interpolation Polynomial and Green Functions -- 1.3.2 Inequalities for n-Convex Functions at a Point -- 1.3.3 Bounds for Remainders and Functionals -- 1.4 Linear Inequalities and the Fink Identity with New Green Functions -- 1.4.1 Results Obtained by the Fink identity and New Green functions -- 1.4.2 Inequalities for n-Convex Functions at a Point -- 1.4.3 Bounds for Remainders and Functionals -- 1.5 Linear Inequalities and the Abel-Gontscharoff's Interpolation Polynomial -- 1.5.1 Results Obtained by the Abel-Gontscharoff's Interpolation -- 1.5.2 Results Obtained by the Abel-Gontscharoff's Interpolation Polynomial and Green Functions -- 1.5.3 Inequalities for n-Convex Functions at a Point -- 1.5.4 Bounds for Remainders and Functionals -- 2 Ostrowski Inequality -- 2.1 Generalized Ostrowski Type Inequalities with Parameter. ; 2.1.1 Ostrowski Type Inequality for Bounded Differentiable Functions -- 2.1.2 Ostrowski Type Inequalities for Bounded Below Only and Bounded Above Only Differentiable Functions -- 2.1.3 Applications to Numerical Integration -- 2.2 Generalized Ostrowski Type Inequalities for Functions of Lp Spaces and Bounded Variation -- 2.2.1 Ostrowski Type Inequality for Functions of Lp Spaces -- 2.2.2 Ostrowski Type Inequality for Functions of Bounded Variation -- 2.2.3 Applications to Numerical Integration -- 2.3 Generalized Weighted Ostrowski Type Inequality with Parameter -- 2.3.1 Weighted Ostrowski Type Inequality with Parameter -- 2.3.2 Applications to Numerical Integration -- 2.4 Generalized Weighted Ostrowski-Grüss Type Inequality with Parameter -- 2.4.1 Weighted Ostrowski-Grüss Type Inequality with Parameter by Using Korkine's Identity -- 2.4.2 Applications to Probability Theory -- 2.4.3 Applications to Numerical Integration -- 2.5 Generalized Fractional Ostrwoski Type Inequality with Parameter -- 2.5.1 Fractional Ostrowski Type Inequality Involving Parameter -- 2.6 Generalized Inequalities for Functions of Lp Spaces via Montgomery Identity with Parameters -- 2.6.1 Montgomery Identity for Functions of Two Variables involving Parameters -- 2.6.2 Generalized Ostrowski Type Inequality -- 2.6.3 Generalized Grüss Type Inequalities -- 3 Functions with Nondecreasing Increments -- 3.1 Functions with Nondecreasing Increments in Real Life -- 3.2 Relationship Among Functions with Nondecreasing Increments and Many Others -- 3.3 Functions with Nondecreasing Increments of Order 3 -- 3.3.1 On Levinson Type Inequalities -- 3.3.2 On Jensen-Mercer Type Inequalities -- 4 Popoviciu and Čebyšev-Popoviciu Type Identities and Inequalities -- 4.1 Linear Inequalities for Higher Order -Convex and Completely Monotonic Functions. ; 4.1.1 Discrete Identity for Two Dimensional Sequences -- 4.1.2 Discrete Identity and Inequality for Functions of Two Variables -- 4.1.3 Integral Identity and Inequality for Functions of One Variable -- 4.1.4 Integral Identity and Inequality for Functions of Two Variables -- 4.1.5 Mean Value Theorems and Exponential Convexity -- Mean Value Theorems -- Exponential Convexity -- Examples of Completely Monotonic and Exponentially Convex Functions -- 4.2 Generalized Čebyšev and Ky Fan Identities and Inequalities for -Convex Functions -- 4.2.1 Generalized Discrete Čebyšev Identity and Inequality -- 4.2.2 Generalized Integral Čebyšev Identity and Inequality -- 4.2.3 Generalized Integral Ky Fan Identity and Inequality -- 4.3 Weighted Montgomery Identities for Higher Order Differentiable Function of Two Variables and Related Inequalities -- 4.3.1 Montgomery Identities for Double Weighted Integrals of Higher Order Differentiable Functions -- Special Cases -- 4.3.2 Ostrowski Type Inequalities for Double Weighted Integrals of Higher Order Differentiable Functions -- 4.3.3 Grüss Type Inequalities for Double Weighted Integrals of Higher Order Differentiable Functions -- Bibliography -- Index.
• Titolo autorizzato: New perspectives on the theory of inequalities for integral and sum
• ISBN: 3-030-90563-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910558484803321
• Lo trovi qui: Univ. Federico II