Fixed Point Theory and its Applications to Real World Problems

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Anita Tomar (Editor) – Professor and Head, Government Degree College Thatyur, Tehri Garhwal (Uttarakhand), India
M. C. Joshi (Editor) – Professor and Head, Kumaun University Nainital, India

Series: Mathematics Research Developments

BISAC: MAT028000

Fixed-point theory initially emerged in the article demonstrating existence of solutions of differential equations, which appeared in the second quarter of the 18th century (Joseph Liouville, 1837). Later on, this technique was improved as a method of successive approximations (Charles Emile Picard, 1890) which was extracted and abstracted as a fixed-point theorem in the framework of complete normed space (Stefan Banach, 1922). It ensures presence as well as uniqueness of a fixed point, gives an approximate technique to really locate the fixed point and the a priori and a posteriori estimates for the rate of convergence. It is an essential device in the theory of metric spaces. Subsequently, it is stated that fixed-point theory is initiated by Stefan Banach. Fixed-point theorems give adequate conditions under which there exists a fixed point for a given function and enable us to ensure the existence of a solution of the original problem. In an extensive variety of scientific issues, beginning from different branches of mathematics, the existence of a solution is comparable to the existence of a fixed point for a suitable mapping.

The book “Fixed Point Theory & its Applications to Real World Problems” is an endeavour to present results in fixed point theory which are extensions, improvements and generalizations of classical and recent results in this area and touches on distinct research directions within the metric fixed-point theory. It provides new openings for further exploration and makes for an easily accessible source of knowledge. This book is apposite for young researchers who want to pursue their research in fixed-point theory and is the latest in the field, giving new techniques for the existence of a superior fixed point, a fixed point, a near fixed point, a fixed circle, a near fixed interval circle, a fixed disc, a near fixed interval disc, a coincidence point, a common fixed point, a coupled common fixed point, amiable fixed sets, strong coupled fixed points and so on, utilizing minimal conditions. It offers novel applications besides traditional applications which are applicable to real world problems. The book is self-contained and unified which will serve as a reference book to researchers who are in search of novel ideas. It will be a valued addition to the library.

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Preface

Chapter 1. Dynamical Behavior of Generalized Logistic System Using Superior Fixed Point Feedback System
(Ashish, Khamosh and Vinod Kumar – Department of Mathematics, Government College Satnali, Mahendergarh, India, et al.)

Chapter 2. On A New Type of Lipschitz Mapping Pairs in Fixed Point Considerations and Applications
(Ravindra K. Bisht – Department of Mathematics, National Defence Academy, Khadakwasla, Pune, India)

Chapter 3. On Geometric Properties of Non-Unique Fixed Points in b−Metric Spaces
(Meena Joshi, Anita Tomar and S. K. Padaliya – S.G.R.R. (P.G.) College Dehradun, India, et al.)

Chapter 4. Fixed Point Theorem for Multivalued Mappings with Rational Expressions in Complete Partial Metric Spaces
(Santosh Kumar and Terentius Rugumisa – Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Tanzania, et al.)

Chapter 5. Common Fixed Point Theorems In Menger PM-Spaces with Nonlinear Generalized Type
(Rale M. Nikolić, Siniša N. Ješić and Vladimir T. Ristić – Belgrade Metropolitan University, Belgrade, Serbia, et al.)

Chapter 6. Coincidence Point Theorems for Non-Expansive Type Mappings and an Application to Dynamic Programming
(N. Chandra, Mahesh C. Joshi, Bharti Joshi and N. K. Singh – Department of Mathematics, S. N. S. Govt. PG College, Narayan Nagar, Pithoragarh, India, et al.)

Chapter 7. Some Stability and Data Dependence Results for Pseudo-Contractive Multivalued Mappings
(Abdessalem Benterki – LMP2M Laboratory, Department of Mathematics, University of Medea, Medea, Algeria)

Chapter 8. Multivalued Geraghty Θ-Contractions and Applications to Fractional Differential Inclusions
(Said Beloul – Exact Sciences Faculty, University of El Oued, Algeria)

Chapter 9. Near Fixed Point, Near Fixed Interval Circle and Near Fixed Interval Disc in Metric Interval Space
(Anita Tomar and Meena Joshi – Government Degree College Thatyur (Tehri Garhwal), Uttarakhand, India, et al.)

Chapter 10. Applications of Generalized α− Ćirić and α−Browder Contractions in Partial Metric Spaces
(Anita Tomar, Meena Joshi, Venkatesh Bhatt and Giniswamy – Government Degree College Thatyur (Tehri Garhwal), Uttarakhand, India, et al.)

Chapter 11. Fixed Point Theorems for Asymptotically Regular Maps in Partial Metric Spaces
(R. Kumar, Mahesh C. Joshi and N. Garakoti – Department of Mathematics, D. S. B. Campus, Kumaun University, Nainital, India)

Chapter 12. Existence of Common Fixed Point in Quasi-Partial Metric with Applications
(Shivangi Upadhyay, Anita Tomar, Ritu Sharma and Meena Joshi – Uttrakhand Open University, Haldwani, India, et al.)

Chapter 13. An Iterative Algorithm for Weak Contraction Mappings
(N. Garakoti, Mahesh C. Joshi and R. Kumar – Department of Mathematics, D. S. B. Campus, Kumaun University, Nainital, India)

Chapter 14. Fixed Point Stability of Additive Functional Equations in Paranormed Spaces
(Kavita, Sanjay Kumar and Sushma – Department of Mathematics, Deenbandhu Chhotu Ram University of Science and Technology, Murthal, Sonepat, Haryana, India, et al.)

Chapter 15. Amiable Fixed Sets and Their Descriptive Proximities: An Introduction
(James F. Peters – Computational Intelligence Laboratory, University of Manitoba, Winnipeg, Canada and Department of Mathematics, Adiyaman University, Adiyaman, Turkey)

Chapter 16. Strong Coupled Fixed Points of Kannan Type and Reich Type Cyclic Coupled Mappings in S-Metric Spaces
(G. V. R. Babu, P. Durga Sailaja and G. Srichandana – Department of Mathematics, Andhra University, Visakhapatnam, India, et al.)

Chapter 17. A Common Fixed Point Theorem for a Pair of Mappings in Fuzzy Metric Spaces with an Application
(Ayush Bartwal and R.C. Dimri – Department of Mathematics, H.N.B. Garhwal University, Uttarakhand, India)

Chapter 18. Coupled Common Fixed Point Theorems for Geraghty Contraction Mappings Satisfying Mixed Weakly Monotone Property in Sb-Metric Space
(N. Priyobarta and Yumnam Rohen – National Institute of Technology, Manipur, Imphal, India)

Chapter 19. Fixed Point Theorems for Multivalued Suzuki Type Z_R-Contraction in Relational Metric Space
(Swati Antal, Deepak Khantwal and U. C. Gairola – H.N.B. Garhwal University, BGR Campus Pauri Garhwal, Uttarakhand, India, et al.)

Chapter 20. w-Interpolative Hardy-Rogers Type Contractions on Quasi-Partial b-Metric Space
(Pragati Gautam, Vishnu Narayan Mishra, Swapnil Verma and Rhythm Parija – Department of Mathematics, Kamala Nehru College, University of Delhi, August Kranti Marg,
New Delhi, India, et al.)

Chapter 21. General Three-Step Iteration Process (nv) for Suzuki Generalized Nonexpansive Mappings
(Nisha Sharma and Lakshmi Narayan Mishra – Department of Mathematics, Pt. J.L.N. Govt. College, Faridabad, India, et al.)

Chapter 22. A Generalized Fixed Point Theorem on Partial b-Metric Spaces
(Anita Kumari and Deepak Kumar – Department of Mathematics, D. S. B. Campus, Kumaun University, Nainital, India)

Chapter 23. Fixed point to fixed disc and application in partial metric spaces
(Meena Joshi, Anita Tomar and S. K. Padaliya – S.G.R.R. (P.G.) College Dehradun, India, et al.)

Index

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