Recent Advances in Fixed Point Theory and Applications



Series: Mathematics Research Developments
BISAC: MAT000000

Fixed point theory is a growing and exciting branch of mathematics with a variety of wide applications in biological and mathematical sciences, proposing newer applications in discrete dynamics and super fractals. The present endeavor is to report the latest trend in metric fixed point theory, emphasizing newer applications in numerical analysis, discrete dynamics and fractal graphics, besides traditional applications. The book is useful to a large class of readers interested in analysis, applicable mathematics and fractal graphics. The articles have been selected carefully so that the book is useful for sophomores up to senior researchers looking for new material and new ideas in the existence of fixed points, new applications and survey articles. A few chapters included herein are formal in nature and suggest new directions of research in this area, which are especially useful to beginners in the field. (Imprint: Nova)

Table of Contents

Table of Contents


Chapter 1. Mean-Type Mappings Involving Generalized Weighted Classical Means, Their Iterations and Invariant Means
Janusz Matkowski (Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Zielona Góra, Poland)

Chapter 2. Common Fixed Point Theorems for Reciprocally Continuous System of Maps
Umesh Chandra Gairola and Deepak Khantwal (Department of Mathematics, H. N. B. Garhwal University, BGR Campus, Pauri Garhwal, Uttarakhand, India)

Chapter 3. On Weakly Uniformly Strict Contractions
Ashish Kumar and Shyam Lal Singh (Department of Mathematics, Himalayan School of Engineering and Technology, SRHU, and others)

Chapter 4. Recent Developments in Metric Fixed Point Theory for Multivalued Mappings
Shyam Lal Singh and Rajendra Pant (Govind Nagar, Rishikesh, and others

Chapter 5. Existence and Convergence Results for Generalized -Nonexpansive Mappings in Hyperbolic Metric Spaces
Rajendra Pant, Rahul Shukla and Shyam Lal Singh (Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, India, and others)

Chapter 6. A New Type of Suzuki Fixed Point Theorem for Fuzzy Mappings in Ordered Metric Spaces
Raj Kamal and Shyam Lal Singh (Department of Mathematics, Government postgraduate College, Kanwali, Rewari, India, and others)

Chapter 7. C-Class Function on Some Fixed Point Theorems for Certain Contractive Mappings on Metric and Generalized Metric Spaces
Arslan Hojat Ansari, Brian Fisher and M. S. Khan (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran, and others)

Chapter 8. Fixed Points under a New Commuting Condition
Abhijit Pant, R. P. Pant and M. C. Joshi (Department of Mathematics, DSB Campus, Kumaun University, Nainital, India)

Chapter 9. Rhoades-Type Fixed Point Theorem in Partial Metric Spaces
Santosh Kumar and Terentius Rugumisa (Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Tanzania, and others)

Chapter 10. Coincidence Point Theorems for Generalized Contraction in Partial Metric Spaces
N. Chandra, M. C. Arya and Mahesh C. Joshi (Department of Mathematics, DSB Campus, Kumaun University, Nainital, India)

Chapter 11. Common Fixed Point Theorems with an Application
Anita Tomar, Shivangi Upadhyay and Ritu Sharma (Government P.G. College Dakpathar, Dehradun (Uttarakhand), India)

Chapter 12. A Coupled Coincidence Point Theorem in Multiplicative Metric Spaces
P. P. Murthy abd Rashmi (Department of Pure and Applied Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur (Chhatisgarh), India)

Chapter 13. The Dhage Iteration Method for Initial Value Problems of Nonlinear First Order Hybrid Functional Integrodifferential Equations
Bapurao C. Dhage, Kasubai (Gurukul Colony, Maharashtra, India)

Chapter 14. The Dhage Iteration Method for Nonlinear First Order Hybrid Functional Integrodifferential Equations with a Linear Perturbation of the Second Type
Bapurao C. Dhage, Shyam B. Dhage and Namdeo S. Jadhav (Kasubai, Gurukul Colony, Dist. Latur, Maharashtra, India)

Chapter 15. An Application of Fixed Point Theorems to Local Attractivity of Certain Functional Integral Equation Solutions
Hemant Kumar Pathak and Ekta Tamrakar (S.o.S. in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.), India)

Chapter 16. Cubic Superior Mandelbrot Sets
Mamta Rani (Central University of Rajasthan, Kishangarh, Rajasthan, India)

Chapter 17. Darboux and Cellerier Fractal Hedgehogs
Mamta Rani, R. C. Dimri and Darshana J. Prajapati (Central University of Rajasthan, Kishangarh, Rajasthan, India, and others)

Chapter 18. Noor Transcendental Julia and Mandelbrot Sets
Bharti Singh, Mamta Rani and Ashish (IFTM University, Moradabad, UP, India, and others)

Chapter 19. Generation of Superfractals Using Superior Iterations
Sarika Jain (Amity Institute of Information Technology, Amity University Uttar Pradesh, Noida, India)

Chapter 20. Dynamics of a Family of Nonlinear Mappings
Abhijit Pant and R. P. Pant (Department of Mathematics, DSB Campus, Kumaun University, Nainital, India)

Chapter 21. A New Approach to Solving Equations in Numerical Praxis
S. L. Singh and Govind Nagar (Rishikesh, India)

Chapter 22. Approximate Fixed Points in b-Metric Spaces
M. O. Olatinwo (Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria)



“This book is a nice collection of research papers on Fixed Point Theory and Applications. Researchers in this field will find this volume invaluable because of the impact it has on practical applications. This book has been very beneficial for me and I highly recommend it for anyone interested in learning more about the subject.” – Ravi P. Agarwal, Professor and Chair of the Department of Mathematics, Texas A&M University-Kingsville, Texas

“The book Recent Advances in Fixed Point Theory and Applications proposes several actual and important topics in nonlinear analysis. Fixed point problems, common fixed point problems, coincidence point problems, coupled coincidence problems are considered in various contexts and for different classes of single-valued and multi-valued operators. A consistent part is dedicated to the applications of the theoretical results. Different types of operator equations and applications to the mathematics of fractals are discussed. This book is an inspired choice of both the editors and the publishing house. The book will be useful to students and researchers in nonlinear analysis and related fields.” – Adrian Petruºel, Professor, Faculty of Mathematics and Computer Science, Babeș-Bolyai University Cluj-Napoca , Romania

“This book in a comprehensive way presents interesting contributions by well-established as well as young authors to different aspects of fixed point theory and its applications. Self-contained and unified in presentation, the book touches upon a wide range of areas that include solutions of functional integral equations and fractals apart from the results which deal with the existence of coincidence and common fixed points of various classes of mappings in different settings. The book will serve as a reference book to researchers in fixed point theory and will be a valuable addition to any library.” – S. N. Mishra, Professor Emeritus, Department of Mathematics, Walter Sisulu University, South Africa

“The contributions in this book have significant, interesting and novel applications of the fixed point theory in various branches of mathematics, physics and engineering sciences. The emphasis is given to interdisciplinary research. All the articles in this volume are treated in a unified and self-contained manner, which can be viewed as innovative style. Presentation of the techniques, theory and applications make this book an invaluable references for researchers and other professional interested in pure and applied sciences. Some papers published in this volume will be useful for graduate students and researchers, who are interested in latest information. Applications of the fixed points theory in fractal geometry and other branches are novel one and will have important impact in the developments of fixed point theory. These developments may be regarded a stranding point for future research.” – Muhammad Aslam Noor, Eminent Professor, Department of Mathematics, Islamabad Campus, COMSATS Institute of Information Technology, Islamabad, Pakistan

“Fixed Point Theory is the cornerstone of Topology, Functional Nonlinear Analysis and Applied Sciences. The crucial role of fixed point theory in quantitative sciences make it attractive in researchers. As a consequence of its charm, this theory has been improved so fast in the last decades and several nice results have been announced. Among them, the recent book of Umesh Chandra Gairola and Rajendra Pant, Recent Advances in Fixed Point Theory and Applications, has a special place due to expressing of the connections between the theory and practice with concrete examples of applications.” – Erdal Karapinar, Professor of Mathematics, ATILIM University, Ankara, Turkey


The book is useful to a large class of readers having interest in analysis, applicable mathematics and fractal graphics.

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