A new iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contractive mappings and its application

In this paper, we introduce a new iterative scheme for finding a common element of the set of a solution of an equilibrium problem and the set of fixed points of finite family strict pseudo-contraction mappings in a real Hilbert space. Some strong convergence theorems are established using the iterative scheme. In the meantime, we successfully apply these Theorems to find a common element of the set of a solution of an equilibrium problem and the set of fixed points of finite family of non-expansive mappings in a real Hilbert space. The results in this paper improve the corresponding ones of [3,6] and references therein

Theory and Application of Fixed Point

In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications

Nonlinear Analysis and Optimization with Applications

Nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, variational analysis, nonlinear optimization, convex analysis, nonlinear ordinary and partial differential equations, dynamical system theory, mathematical economics, game theory, signal processing, control theory, data mining, and so forth. Optimization problems have been intensively investigated, and various feasible methods in analyzing convergence of algorithms have been developed over the last half century. In this Special Issue, we will focus on the connection between nonlinear analysis and optimization as well as their applications to integrate basic science into the real world