Mathematical Analysis I: Approximation Theory: ICRAPAM 2018, New Delhi, India, October 23–25 (Springer Proceedings in Mathematics & Statistics)

This book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23–25 October 2018. Divided into two volumes, it discusses major topics in mathematical analysis and its applications, and demonstrates the versatility and inherent beauty of analysis. It also shows the use of analytical techniques to solve problems and, wherever possible, derive their numerical solutions. This volume addresses major topics, such as operator theory, approximation theory, fixed-point theory, holomorphic functions, summability theory, and analytic functions. It is a valuable resource for students as well as researchers in mathematical sciences. Preface Contents About the Editors Expressions, Localization Results, and Voronovskaja Formulas for Generalized Durrmeyer Type Operators 1 Introduction 2 Durrmeyer Type Operators 3 Localization Results 4 Voronovskaja Type Formulas 5 Further Remarks 5.1 Mixed Summation Integration Operators 5.2 Multivariate Durrmeyer Operators References Lupaş–Kantorovich Type Operators for Functions of Two Variables 1 Introduction 2 Basic Results 3 Main Results References Bernstein Polynomial Multiwavelets Operational Matrix for Solution of Differential Equation 1 Introduction 2 Wavelets and Bernstein Polynomial Multiwavelets 3 Function Approximation 4 Bernstein Polynomial Multiwavelets Operational Matrix of Integration 5 Method of Solution 6 Illustrative Examples 6.1 Example 1 6.2 Example 2 7 Conclusion References Convergence Estimates of Certain Exponential Type Operators 1 Introduction 2 Moment Estimation 3 Convergence Estimates References A Better Error Estimation on Generalized Positive Linear Operators Based on PED and IPED 1 Introduction 2 Basic Results 3 Voronovskaya Type Results References Q-Analogue of Generalized Bernstein–Kantorovich Operators 1 Introduction 2 Basic Results 3 Main Results References Approximation by Certain Operators Linking the α-Bernstein and the Genuine α-Bernstein–Durrmeyer Operators 1 Introduction 2 Approximation Properties of Un,αρ Operators 3 Voronovskaja Type Theorem References Note on a Proof for the Representation of the kth Order Kantorovich Modification of Linking Baskakov Type Operators 1 Introduction References Degree of Approximation by Generalized Boolean Sum of λ-Bernstein Operators 1 Introduction 2 Preliminaries 3 Main Results 4 Bivariate Extension of the Operator 5 Degree of Approximation 6 GBS of the Operator Bm,n,λ1,λ2 References Durrmeyer Modification of Lupaş Type Baskakov Operators Based on IPED 1 Introduction 2 Auxiliary Results 3 Direct Results References On Bernstein–Chlodowsky Type Operators Preserving Exponential Functions 1 Introduction 2 Preliminary Results 3 Quantitative Results 4 Variation Detracting Property of Bernstein–Chlodowsky Operators References Iterative Approximation of Common Fixed Points in Kasahara Spaces 1 Introduction 2 Basic Notions and Notations 3 Main Results References Fixed Point Theorem in Fuzzy Metric Space Via α-Series Contraction 1 Introduction 2 Preliminaries 3 Main Result 4 Application 5 Future Scope References The Unique Common Fixed Point Theorem for€Four Mappings Satisfying Common Limit in€the€Range Property in€b-Metric Space 1 Introduction 2 Preliminary 2.1 b-Metric Space [12, 13] 2.2 . 2.3 Common Limit in€the€Range Property [21] 2.4 Altering Distance Function [27] 2.5 Weakly Compatible Map [17] 3 Main Theorem References Radius Estimates for Three Leaf Function and Convex Combination of Starlike Functions 1 Introduction 2 mathcalS*3 mathcalL-Radii for Several Classes 3 mathcalSEL* Radius Estimates References First-Order Differential Subordinations for Janowski Starlikeness 1 Introduction 2 Subordination Results Associated with Lune 3 Further Results References Coefficient Bounds for a Unified Class of Holomorphic Functions 1 Introduction and Preliminaries 2 Main Results References Bohr Radius for Certain Analytic Functions 1 Introduction 2 Bohr Radius for the Class of α-Spiral Functions of Order ρ 3 Bohr Radius for Second-Order Differential Subordination References Third Hankel Determinant for Certain Classes of Analytic Functions 1 Introduction 2 Third Hankel Determinant References μ-Statistical Convergence of Sequences in Probabilistic n-Normed Spaces 1 Introduction 2 Preliminaries 3 μ-Statistical Convergence and μ-Density Convergence in PnN-Spaces 4 μ-Statistical Limit Points in PnN-Spaces 5 Conclusion References Lacunary Statistical Convergence of Order α for Generalized Difference Sequences and Summability Through Modulus Function 1 Introduction 2 Definitions Related to Our Work 3 Main Results on Sθα (Δvm) & Nθα( Δvm, p) 4 Results on Space ωθα(Δvm,f,p) References Convergence of Three-Step Iterative Process for Generalized Asymptotically Quasi-nonexpansive Mappings in CAT(0) Spaces 1 Introduction 2 Main Results References