We show a unified form of two fixed point theorems and a unified form of a fixed point theorem and a minimax inequality.We also apply our results to show the existence of solutions of generalized quasi-variational inequalities.

The paper is concerned with the problem of finding a common solution of a variational inequality problem governed by Lipschitz continuous monotone mappings and a fixed point problem of nonexpansive mappings. To solve this problem, we introduce a new iterative algorithm which is based on Tseng's extragradient method. Moreover we prove the strong convergence of the algorithm to a solution of the above-stated problem without the hypothesis of the asymptotical regularization.

The purpose of this paper is to use a modified hybrid algorithm for finding a minimizer of a non-smooth composite minimization problem in Banach spaces. Without the assumptions that the potential function is Frchet differentiable and its gradient is L-Lipschitz continuous, we prove that the iterative sequence generated by the hybrid algorithm converges strongly to a minimizer of the composite optimization problem in Banach spaces.

Between two adjacent zeros of any nontrivial solution of the second order ordinary differential equation x (t) + a(t)x (t) + b(t)x(t) = 0 there is one and only one zero of every nonproportional solution. This principle of zeros' distribution is known as the Sturm separation theorem which is a basis of many classical results on oscillation and asymptotic properties and on boundary value problems for ordinary differential equations. For delay and integro-differential equations this principle of zeros' distribution is not true. In this paper, the assertion on validity of the Sturm separation theorem are proposed. Distance between two zeros of nontrivial solutions to integro-differential equations is estimated.

In this paper, we introduce and study a new class of analytic and multivalent (p-valent) functions involving higherorder derivatives. For this multivalent function class, we derive several interesting properties including coefficient inequalities, distortion theorems and extreme points. Several applications involving an integral operator are also considered. Finally, we obtain some results for the modified Hadamard product of functions belonging to the multivalent function class introduced in this paper. Relevant connections of the results presented in this paper with those in a number of other related works on this subject are also pointed out.

in celebration of his 70th birthday.During his research career Professor Reich has made significant contributions to many areas of mathematics including nonlinear operator theory, nonlinear evolution and integral equations, the identification and estimation of nonlinear distributed parameter systems, infinitedimensional holomorphy, variational inequalities, and sequential and parallel algorithms in feasibility and optimization.His list of publications contains three monographs, nineteen edited volumes and more than 450 research papers.His work has had great impact on research in analysis and optimization, as well as on a wide range of their applications.Simeon has had fifteen PhD students and nine MSc students.In this special issue we present papers authored by a selected group of experts in the areas of nonlinear analysis and optimization theory.Most of the papers collected here have been contributed by collaborators, friends and colleagues of Simeon's, who were influenced by his research.Part II of the special issue contains nine papers contributed by well-known experts in nonlinear analysis and optimization from Canada, Egypt, Germany, Israel, Japan, Nigeria, Romania and USA.These papers cover a wide spectrum of important problems and topics of current research interest of analysis and optimization such as maximally monotone operators derived from nonsunny nonexpansive retractions; modulated ergodic theorems; proximal point algorithm in CAT(0) spaces; A Krasnoselskii-type algorithm for approximating solutions of variational inequality problems and convex feasibility problems; Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers; Sturm theorems and distance between adjacent zeros for second order integro-differential equations; disintegration of Young measures; Edelstein's fixed point theorem in semimetric spaces and a second order finite difference scheme for a variable infection-structured model of mycobacterium marinum dynamics in aquatic animals.Therefore we feel that this special issue will be very valuable for many mathematicians and practitioners who are interested in recent developments in nonlinear analysis and optimization as well as their numerous applications.

In this paper, we use the dual variable to propose two algorithms for split common fixed-point problems of averaged mappings in real Hilbert spaces. Under suitable conditions, weak and strong convergence theorems are established. Finally, we give numerical experiments to illustrate the efficiency of the proposed iterative algorithms.

Let (X, G) be a generalized metric space. Let {G n } nN be a sequence of G-metrics on X and let T n : X n X n , where {X n } is a sequence of nonempty subsets of X, be a (, )-weakly contractive mapping with a fixed point x n . In this paper, we study the the convergence of {T n } and the convergence of {x n }. Various stability results are established.

In this paper, a non-autonomous differential system with state delays and with a large coefficient for the control (high gain control) is considered. By a proper control transformation, this system is converted into equivalent time delay system singularly perturbed by a small positive parameter. The latter system, is decomposed asymptotically into two much simpler parameter-free subsystems, slow and fast ones. The slow subsystem has delays in the state and control variables, while the fast subsystem is delay-free. Based on the assumption of the Euclidean space controllability of the slow subsystem, the Euclidean space controllability of the transformed and original systems is established for all sufficiently small values of the parameter of singular perturbation. Also, the minimum energy control problem for the transformed system is considered. Asymptotic behaviour with respect to the small parameter of the solution to this problem is studied. An illustrative example is presented.