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.

Table of Contents:
Preface; Dynamical Behavior of Generalized Logistic System Using Superior Fixed Point Feedback System; On A New Type of Lipschitz Mapping Pairs in Fixed Point Considerations and Applications; On Geometric Properties of Non-Unique Fixed Points in b−Metric Spaces; Fixed Point Theorem for Multivalued Mappings with Rational Expressions in Complete Partial Metric Spaces; Common Fixed-Point Theorems In Menger PM-Spaces with Nonlinear Generalized Type; Coincidence Point Theorems for Non-Expansive Type Mappings and an Application to Dynamic Programming; Some Stability and Data Dependence Results for Pseudo-Contractive Multivalued Mappings; Multivalued Geraghty Θ-Contractions and Applications to Fractional Differential Inclusions; Near Fixed Point, Near Fixed Interval Circle and Near Fixed Interval Disc in Metric Interval Space; Applications of Generalized α− Ćirić and α−Browder Contractions in Partial Metric Spaces; Fixed Point Theorems for Asymptotically Regular Maps in Partial Metric Spaces; Existence of Common Fixed Point in Quasi-Partial Metric with Applications; An Iterative Algorithm for Weak Contraction Mappings; Fixed Point Stability of Additive Functional Equations in Paranormed Spaces; Amiable Fixed Sets and Their Descriptive Proximities: An Introduction; Strong Coupled Fixed Points of Kannan Type and Reich Type Cyclic Coupled Mappings in S-Metric Spaces; A Common Fixed-Point Theorem for a Pair of Mappings in Fuzzy Metric Spaces with an Application; Coupled Common Fixed-Point Theorems for Geraghty Contraction Mappings Satisfying Mixed Weakly Monotone Property in Sb-Metric Space; Fixed Point Theorems for Multivalued Suzuki Type Z_R-Contraction in Relational Metric Space; w-Interpolative Hardy-Rogers Type Contractions on Quasi-Partial b-Metric Space; General Three-Step Iteration Process (nv) for Suzuki Generalized Nonexpansive Mappings; A Generalized Fixed-Point Theorem on Partial b-Metric Spaces; Fixed point to fixed disc and application in partial metric spaces; Index.