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Intro; Preface; Contents; 1 Moment Generating Functions and Central Moments; 1.1 Some Operators; 1.1.1 Bernstein Operators; 1.1.2 Baskakov Operators; 1.1.3 Szász-Mirakyan Operators; 1.1.4 Lupaş Operators; 1.1.5 Post Widder Operators; 1.2 Kantorovich Type Operators; 1.2.1 Bernstein-Kantorovich Operators; 1.2.2 Baskakov-Kantorovich Operators; 1.2.3 Szász-Kantorovich Operators; 1.2.4 Lupaş-Kantorovich Operators; 1.3 Durrmeyer Type Operators; 1.3.1 Szász-Durrmeyer Operators; 1.3.2 Baskakov-Szász Operators; 1.3.3 Păltǎnea Type Operators; 2 Quantitative Estimates; 2.1 Discrete Operators
2.1.1 Modified Szász-Mirakyan Operators2.1.2 Lupaş-Type Modified Operators; 2.1.3 Modified Baskakov Type Operators; 2.2 Some Integral Operators; 2.2.1 Post-Widder Operators; 2.2.2 Lupaş-Kantorovich Type Modified Operators; 2.2.3 Modified Szász-Kantorovich Operators; 2.2.4 Modified Szász-Durrmeyer Operators; 2.2.5 Modifications of Phillips Operators; 2.3 Better Approximation by Certain Positive Linear Operators; 2.3.1 Bernstein Type Operators; 2.3.2 Bernstein-Durrmeyer Type Operators; 2.3.3 Bézier Variant of the Bernstein-DurrmeyerType Operators; 2.3.4 Bernstein-Stancu Type Operators
2.3.5 Lupaş Operators Based on Pólya Distribution3 Basics of Post-quantum Calculus; 3.1 Introduction; 3.2 Some Notations of q-Calculus; 3.3 Certain Definitions of (p,q)-Calculus; 3.3.1 (p,q)-Beta Function of First Kind; 3.3.2 (p,q)-Beta Function of Second Kind; 3.3.3 (p,q)-Exponential and Gamma Function; 3.4 Some Discrete (p,q) Operators; 4 (p,q)-Integral Operators; 4.1 Kantorovich Type Operators; 4.1.1 (p,q)-Bernstein-Kantorovich Operators; 4.1.2 (p,q)-Baskakov-Kantorovich Operators; 4.1.3 (p,q)-Szász-Mirakyan-Kantorovich Operators; 4.2 Durrmeyer Type Operators
4.2.1 (p,q)-Bernstein-Durrmeyer Operators4.2.2 Limit (p,q)-Bernstein-Durrmeyer Operators; 4.2.3 (p,q)-Baskakov-Durrmeyer Operators; 4.2.4 (p,q)-Szász-Durrmeyer Operators; 4.2.5 (p,q)-Variant of Szász-Beta Operators; 5 Univariate Grüss- and Ostrowski-Type Inequalities for Positive Linear Operators; 5.1 Grüss-Type Inequalities for a Positive Linear Functional; 5.2 Grüss-Type Inequalities for Some Positive Linear Operators; 5.2.1 The Classical Hermite-Fejér Interpolation Operator; 5.2.2 The Convolution-Type Operator; 5.2.3 King Operators; 5.2.4 A Piecewise Linear Interpolation Operator Sn
5.3 Estimates via Cauchy's Mean Value Theorem5.4 Grüss-Type Inequalities on Compact Metric Spaces; 5.5 Grüss Inequalities via Discrete Oscillations; 5.5.1 Applications for Linear Operators; 5.5.2 Grüss-Type Inequalities via Discrete Oscillations for More Than Two Functions; 5.6 Ostrowski Inequalities; 6 Bivariate Grüss-Type Inequalities for Positive Linear Operators; 6.1 Bivariate Linear Operators; 6.1.1 Bivariate Bernstein Operator; 6.1.2 Bivariate Szász-Mirakyan Operators; 6.1.3 Bivariate Baskakov Operators; 6.1.4 Bivariate King Operators
2.1.1 Modified Szász-Mirakyan Operators2.1.2 Lupaş-Type Modified Operators; 2.1.3 Modified Baskakov Type Operators; 2.2 Some Integral Operators; 2.2.1 Post-Widder Operators; 2.2.2 Lupaş-Kantorovich Type Modified Operators; 2.2.3 Modified Szász-Kantorovich Operators; 2.2.4 Modified Szász-Durrmeyer Operators; 2.2.5 Modifications of Phillips Operators; 2.3 Better Approximation by Certain Positive Linear Operators; 2.3.1 Bernstein Type Operators; 2.3.2 Bernstein-Durrmeyer Type Operators; 2.3.3 Bézier Variant of the Bernstein-DurrmeyerType Operators; 2.3.4 Bernstein-Stancu Type Operators
2.3.5 Lupaş Operators Based on Pólya Distribution3 Basics of Post-quantum Calculus; 3.1 Introduction; 3.2 Some Notations of q-Calculus; 3.3 Certain Definitions of (p,q)-Calculus; 3.3.1 (p,q)-Beta Function of First Kind; 3.3.2 (p,q)-Beta Function of Second Kind; 3.3.3 (p,q)-Exponential and Gamma Function; 3.4 Some Discrete (p,q) Operators; 4 (p,q)-Integral Operators; 4.1 Kantorovich Type Operators; 4.1.1 (p,q)-Bernstein-Kantorovich Operators; 4.1.2 (p,q)-Baskakov-Kantorovich Operators; 4.1.3 (p,q)-Szász-Mirakyan-Kantorovich Operators; 4.2 Durrmeyer Type Operators
4.2.1 (p,q)-Bernstein-Durrmeyer Operators4.2.2 Limit (p,q)-Bernstein-Durrmeyer Operators; 4.2.3 (p,q)-Baskakov-Durrmeyer Operators; 4.2.4 (p,q)-Szász-Durrmeyer Operators; 4.2.5 (p,q)-Variant of Szász-Beta Operators; 5 Univariate Grüss- and Ostrowski-Type Inequalities for Positive Linear Operators; 5.1 Grüss-Type Inequalities for a Positive Linear Functional; 5.2 Grüss-Type Inequalities for Some Positive Linear Operators; 5.2.1 The Classical Hermite-Fejér Interpolation Operator; 5.2.2 The Convolution-Type Operator; 5.2.3 King Operators; 5.2.4 A Piecewise Linear Interpolation Operator Sn
5.3 Estimates via Cauchy's Mean Value Theorem5.4 Grüss-Type Inequalities on Compact Metric Spaces; 5.5 Grüss Inequalities via Discrete Oscillations; 5.5.1 Applications for Linear Operators; 5.5.2 Grüss-Type Inequalities via Discrete Oscillations for More Than Two Functions; 5.6 Ostrowski Inequalities; 6 Bivariate Grüss-Type Inequalities for Positive Linear Operators; 6.1 Bivariate Linear Operators; 6.1.1 Bivariate Bernstein Operator; 6.1.2 Bivariate Szász-Mirakyan Operators; 6.1.3 Bivariate Baskakov Operators; 6.1.4 Bivariate King Operators