ADVANCES IN NUMBER THEORY AND APPLIED ANALYSIS

Presently, the exploration of the applications of different techniques and tools of number theory and mathematical analysis are extensively prevalent in various areas of engineering, mathematical, physical, biological and statistical sciences. This book will present the most recent developments in these two fields through contributions from eminent scientists and mathematicians worldwide.

The book will present the current state of the art development in these two areas through original new contributions and surveys. As such, readers will find several useful tools and techniques to develop their skills and expertise in number theory and applied analysis. New research directions are also indicated in each of the chapters. This book is meant for graduate students, faculty and researchers willing to expand their knowledge in number theory and mathematical analysis. The readers of this book will require minimum prerequisites of analysis, topology, number theory and functional analysis.

Contents:

• Open Problems in Number Theory (Pradip Debnath)
• Arithmetic and Congruence Properties of Partition Function (Nabanita Konwar)
• Collatz Hypothesis and Kurepa's Conjecture (Nicola Fabiano, Nikola Mirkov, Zoran D Mitrović, and Stojan Radenović)
• On Zeta Functions and Allied Theta Functions (Hongyu Li, Takako Kuzumaki, and Shigeru Kanemitsu)
• Sylvester Sums on the Frobenius Set in Arithmetic Progression with Initial Gaps (Takao Komatsu)
• Arithmetic Properties of Minimal Excludants of Partitions of Integers (Nipen Saikia)
• On Certain ℓ-regular Partitions: A Brief Survey (Chiranjit Ray)
• Some Applications of an Algorithm in Number Theory (Nihal Özgür)
• The Components Exponential Function in Scator Hypercomplex Space: Planetary Elliptical Motion and Three-Body Choreographies (M Fernández-Guasti)
• Caristi-Type Nonunique Fixed-Point Results and Fixed-Circle Problem on b_v(s)-Metric Spaces (Nihal Taş and Ozgur Ege)
• Extended Interpolative Hardy–Rogers–Geraghty–Wardowski Contractions and an Application (Samira Hadi Bonab, Vahid Parvaneh, Zohreh Bagheri, and Roghayeh Jalal Shahkoohi)
• (η,ψ)-Rational F-Contractions and Weak-Wardowski Contractions in a Triple-Controlled Modular Type Metric Space (Hemant Kumar Nashine, Samira Hadi Bonab, and Vahid Parvaneh)
• Sufficient Conditions for Mittag-Leffler Functions Associated with Conic Regions (Amit Soni and Deepak Bansal)
• Results on the Existence of Solutions for Some Controlled Optimization Problems (Savin Treanţă)
• The Theory of Nonabsolute Integrable Function Spaces over R^∞ and Its Various Applications (Hemanta Kalita and Bipan Hazarika)
• Subclass of Analytic Functions Involving Mittag-Leffler Type Borel Distribution Series (P Thirupathi Reddy and B Venkateswarlu)
• Hybrid Accelerated Conjugate Gradient Method for Solving Nonlinear System of Equations (Abubakar Sani Halilu, Arunava Majumder, Mohammed Yusuf Waziri, and Idris Ahmed)
• A Closed Form of Integral Transforms in Terms of Lauricella Function F_A⁽ⁿ⁾ and Their Numerical Simulations (Abdelmajid Belafhal, Halima Benzehoua, and Talha Usman)

Readership: Graduate students and researchers in Number Theory and Applied Analysis.

Key Features:

• The book contains chapters with both survey and original research authored by famous mathematicians across the countries
• Discusses open problems and new advances in number theory. Further, recent developments in applied analysis are presented
• Prerequisites are presented in the beginning of each chapter to make the book self-sufficient as much as possible
• Recent research developments are presented in the subsequent chapters maintaining continuity and relation with previous chapters
• Graduate students, faculty and researchers interested in number theory and applied analysis will find sufficient new tools and techniques in this book to enhance their knowledge. New research directions and open problems are presented