Function Spaces , Fixed Points , Approximations , and Applications

An important branch of nonlinear analysis theory, applied in the study of nonlinear phenomena in engineering, physics, and life sciences, is related to the existence of xed points of nonlinear mappings, to the approximation of xed points of nonlinear operators and of zeros of nonlinear operators, and to the approximation of solutions of variational inequalities. is special issue is focused on the latest achievements on these topics and the related applications. e aim is to present newest and extended coverage of the fundamental ideas, concepts, and important results on the topics below in general function spaces useful in analysis. e search for the solutions of equations (ordinary and partial di erential equations, functional di erential equations, integral equations, etc.) is currently studied in speci c spaces of functions. e choice of xed point theorems to be applied is conditioned by the underlying functions space. We invited the authors to present their original articles that will stimulate the continuing e orts in developing new results in the previous mentioned areas. e selected and published papers can be entered in the following areas.

An important branch of nonlinear analysis theory, applied in the study of nonlinear phenomena in engineering, physics, and life sciences, is related to the existence of xed points of nonlinear mappings, to the approximation of xed points of nonlinear operators and of zeros of nonlinear operators, and to the approximation of solutions of variational inequalities.
is special issue is focused on the latest achievements on these topics and the related applications.
e aim is to present newest and extended coverage of the fundamental ideas, concepts, and important results on the topics below in general function spaces useful in analysis.
e search for the solutions of equations (ordinary and partial di erential equations, functional di erential equations, integral equations, etc.) is currently studied in speci c spaces of functions.
e choice of xed point theorems to be applied is conditioned by the underlying functions space.
We invited the authors to present their original articles that will stimulate the continuing e orts in developing new results in the previous mentioned areas.
e selected and published papers can be entered in the following areas.
(i) Function Spaces.J. R. Acosta-Portilla et al. characterized the family of nonexpansive mappings which are invariant under renormings and they also compared the families of nonexpansive mappings under two equivalent norms.
X. Li et al. de ned and studied some subclasses of multivalent analytic functions of higher order in the unit disc.
ese classes generalize some classes previously studied.
ey obtained coe cient inequalities, distortion theorems, extreme points, and integral mean inequalities.
W. Wang et al. considered the question, what is the appropriate formulation of Godefroy-Shapiro criterion for tuples of operators?And they introduced a new notion about tuples of operators S-mixing, which lies between mixing and weakly mixing.ey also obtained a su cient condition to ensure a tuple of operators to be S-mixing.Moreover, they studied some new properties of S-mixing operators on several concrete Banach spaces.
(ii) Fixed Points.J. Tiammee et al. proved some xed points theorems for multivalued nonself G-almost contractions in Banach spaces with a directed graph and given some examples to illustrate the main results.B. Z. Popovic et al. established a unique xed point theorem for three self-maps under rational type contractive condition.In addition, a unique xed point result for six continuous self-mappings through rational type expression is also discussed.
N. Hussain et al. have highlighted that remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function.For the purpose of extension and modi cation of classical ideas related to Mizoguchi-Takahashi contraction, they de ned generalized Mizoguchi-Takahashi G-contractions and established some generalized xed point theorems regarding these contractions.
(iii) Approximation.I. Altun et al. provided su cient conditions for the existence of a unique common xed point for a pair of mappings T, S de ned on a metric space.Moreover, a numerical algorithm is presented in order to approximate such solution.eir approach is di erent from the usually used methods in the literature.J.-P.Sun et al. studied a system of third-order threepoint boundary value problems.By imposing some suitable conditions on the functions, they obtained the existence of at least one positive solution of the system.e main tool used is the theory of the xed point index.
(v) Differential Problems.Q.Sun and Y. Cui investigated a (,  − ) conjugate boundary value problem with integral boundary conditions.By using Mawhin continuation theorem, they studied the solvability of this boundary value problem at resonance.

(
iv) Fixed Point Theory Applied to Differential Problems.Y. Zhang and J. Zhu presented a new nonlinear contraction principle on partial metric spaces and proved the existence of common xed point.ey have also given some examples to apply their results to study the existence of common bounded solution of the system of functional equations.R. Rao and S. Zhong employed Banach xed point theorem to derive LMI-based exponential stability of impulsive Takagi-Sugeno (T-S) fuzzy integrodi erential equations, originated from Cohen-Grossberg Neural Networks.