Advances in Real and Complex Analysis with Applications

This book discusses a variety of topics in mathematics and engineering as well as their applications, clearly explaining the mathematical concepts in the simplest possible way and illustrating them with a number of solved examples. The topics include real and complex analysis, special functions and analytic number theory, q-series, Ramanujan's mathematics, fractional calculus, Clifford and harmonic analysis, graph theory, complex analysis, complex dynamical systems, complex function spaces and operator theory, geometric analysis of complex manifolds, geometric function theory, Riemannian surfaces, Teichmüller spaces and Kleinian groups, engineering applications of complex analytic methods, nonlinear analysis, inequality theory, potential theory, partial differential equations, numerical analysis , fixed-point theory, variational inequality, equilibrium problems, optimization problems, stability of functional equations, and mathematical physics.

It includes papers presented atthe 24th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (24ICFIDCAA), held at the Anand International College of Engineering, Jaipur, 22-26 August 2016. The book is a valuable resource for researchers in real and complex analysis.

Autorentext

MICHAEL RUZHANSKY is a professor at the Department of Mathematics, Imperial College London. He has published over 100 research articles in several leading international journals. He has also published five books and memoirs and nine edited volumes. He has researched topics related to pseudo-differential operators, harmonic analysis and partial differential equations. More recently, he has worked on boundary value problems and their applications. He has been on the editorial board of many respected international journals and served as the President of the International Society of Analysis, Applications, and Computations (ISAAC) in the period 2009-2013.

YEOL JE CHO is a professor at the Department of Mathematics Education, Gyeongsang National University, Korea, and Fellow of the Korean Academy of Science and Technology. He has published over 350 research papers in respected international journals, mainly in the field of fixed point theory, variational inequality problems, equilibrium problems, optimization problems, stability of functional equations and inequality theory. He has been on the editorial boards of several leading journals, such as Fixed Point Theory and Applications, Journal of Nonlinear Science and Applications and 15 more international journal of mathematics and applications. He has also published a number of remarkable books on fixed point theory, stability of functional equations, numerical analysis and degree theory.

PRAVEEN AGGARWAL is a professor at the Department of Mathematics, Anand International College of Engineering, Jaipur, India. He has published over 130 articles related to special functions and fractional calculus in leading mathematics journals, such as Applied Mathematics and Computation, the Journal of Nonlinear Science and Applications, and the Journal of Inequalities and Applications. Recently, he has focused on partial differential equations and fractional differential equations. He has been on the editorial boards of several journals, including SpringerPlus and the Maejo International Journal of Science and Technology. He has been involved in a number of conferences and has also won numerous international research grants such as Research in Group by International Centre for Mathematical Sciences (ICMS) and World Academy of Sciences (TWAS) Visiting Scientist fellowship.

IVÁN AREA is a professor at the Departamento de Matemática Aplicada II, E.E. Aeronáutica e do Espazo Universidade de Vigo, Spain. He has published over 100 articles related to orthogonal polynomials and special functions in leading international journals. His recent research has also focused on fractional analysis and bioinformatics. He has been elected General Secretary of the International Center for Pure and Applied Mathematics (CIMPA), a non-profit organization whose aim is to promote mathematics in developing countries.

Inhalt
Chapter 1. Multiple Gamma Functions and Multiple Hurwitz Zeta Functions.- Chapter 2. Recent Topics on Fixed Point Theory and its Applications.- Chapter 3. Quantizations with and without symmetries.- Chapter 4. Some systems of multivariate orthogonal polynomials.- Chapter 5. Inverse Source problems for Partial Differential Equations involving Fractional Derivatives.- Chapter 6. On Hermite-Fejer Interpolation of Functions of Bounded Variation.- Chapter 7. Step Forward in Fractional Calculus: Theory, Methods and Applications.- Chapter 8. Recent Results on Fractional Order Chaotic Systems.- Chapter 9. Quadratic reciprocity and Riemann's non-differentiable function.- Chapter 10. Integrability theorem for Weyl Algebra and its relation with the Heisenberg Uncertainty Principle.- Chapter 11. Beta Functions Of First And Double Summation Formulae.- Chapter 12. Non-Linear Differential Polynomials Sharing Small Function With Finite Weight.- Chapter 13. On the Inverse of Pesudi-Differential Operators on S1.- Chapter 14. Certain Image Formulas Of Generalized K-Bessel Function.- Chapter 15. Polar Coordinate Form of Bicomplex Number System In Clifford Analysis.- Chapter 16. Existence Theorems Of Generalized Quasi-Variational-Like Inequalities For Upper Hemi-Continuous And Pseudo-Monotone Type Ii Operators On Non-Compact Sets.- Chapter 17. Certain Class Of Meromorphically Multivalent Functions Defined By A Differential Operator.- Chapter 18. An Extension Of The Shannon Wavelet For Numerical Solution Of Integro-Differential Equations.- Chapter 19. A Problem with Two Nonlocal Boundary Conditions for a Mixed Type Equation with Singular Coefficient.- Chapter 20. The Univalently Solvability Of One Nonlocal Boundary Value Problem With Variable Coeffcients For The Mixed Type Equation Of The Second Kind Of The Second Order In A Rectangle.- Chapter 21. A Study of Generalized Fractional Differentiation for Saigo Operators Involving a Multivariable Polynomial, H-Function and the Aleph Function.- Chapter 22. Graphical and Database Analysis of Generalized K-Mittag-Leer Function with MATLAB Implementation.