ON A CLASS OF GENERALIZED NONLINEAR IMPLICIT QUASIVARIATIONAL INCLUSIONS

In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is Proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given, As special cases, some known results in this field are also discussed.

NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.

A system of general nonlinear variational inclusions in Banach spaces

A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces.

A New System of Generalized Variational Inclusions Involving H-η-monotone Operators in Uniformly Smooth Banach Spaces

In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-η-monotone opera- tors, we prove the approximation solvability of solutions using an iterative algorithm. The results in this paper extend and improve some known results from the literature.

Algorithm of solutions for generalized nonlinear implicit quasivariational inclusions with fuzzy mappings

A class of generalized implicit quasivariational inclusions with fuzzy mappings in Hilbert space is discussed in this paper which proves an existence theorem of the solutions and proposes a new iterative algorithm and the convergence of the iterative sequence generated by the new algorithm. These results extend and improve some recent corresponding achievements.

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

PROXIMAL POINT ALGORITHM WITH ERRORS FOR GENERALIZED STRONGLY NONLINEARQUASIVARIATIONAL INCLUSIONS

In this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone; mapping in Hilbert space, an existence theorem of solutions for generalized strongly nonlinear quasivariational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly, nonlinear quasivariational inclusion. As special cases, some known results in this field are also discussed.

GENERALIZED VARIATIONAL PRINCIPLE ON NONLINEAR THEORY OF NATURALLY CURVED AND TWISTED CLOSED THIN-WALLED COMPOSITE BEAMS

Naturally curved and twisted closed thin-walled slender beams of composite material undergoing small strains, large displacements and rotations have been investigated, and an incomplete generalized variational function on theory of elasticity with finite displacement is established far these beams with complete constrained boundaries at two ends. The balance equations as well as all boundary conditions concerned have been deduced from functional stationary value condition. The above-mentioned method can also be extended to other various incomplete constrained boundaries conveniently. In addition, the fundamental equations and concerned formulas in the small displacement theory of the beams can be derived by using above results.

APPROXIMATE SOLUTION TO A CLASS OF MULTIVALUED NONLINEAR MIXED VARIATIONAL INCLUSIONS

Concerned with the existence and convergence properties of approximate solution to multivalued nonlinear mixed variational inclusion problem in a Hilbert space, we established the equivalence between the variational inclusion and the general resolvent equations, obtained three iterative algorithms, provided the convergence analysis of the algorithms. The results obtained improve and generalize a number of resent results.

THE APPLICATIONS OF GENERALIZED VARIATIONAL PRINCIPLES IN NONLINEAR STRUCTURAL ANALYSIS

This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.

Systems of generalized quasi-variational inclusion (disclusion) problems in FC-spaces

By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion （disclusion） problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

Generalized H-η-accretive operators in Banach spaces with application to variational inclusions

In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.

On Generalized Multivalued Random Variational-Like Inclusions

In this paper, we posed a random iterative algorithm for generalized multivalued random variational like inclusions. We define the random relaxed Lipschitz and relaxed monotone mappings and prove the existence and convergence of solutions of the random iterative sequences generated by a random iterative algorithm.

Sensitivity analysis of generalized set-valued quasi-variational inclusion in Banach spaces

The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.

ALGORITHM OF SOLUTIONS FOR MIXEDNONLINEAR VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACE

In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented, An iterative algorithm for approximating the solutions of generalized implicit wriational- like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved,

Implicit Variational Inclusions and Algorithms Involving （A, η）-monotone Operators in 2-uniformly Smooth Banach Spaces

This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving （A, η）-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the （A, η）-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving （H, η）-monotone mappings.

Iterative Algorithm with Mixed Errors for Solving a New System of Generalized Nonlinear Variational-Like Inclusions and Fixed Point Problems in Banach Spaces

A new system of generalized nonlinear variational-like inclusions involving A- maximal m-relaxed η-accretive （so-called, （A, η）-accretive in [36]） mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed ~/-accretive mappings due to Lan et al., the exis- tence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings 81 and 82 and using the resolvent operator technique associated with A-maximal m-relaxed ~？-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q = （S1, S2） which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions, The results presented in this paper extend and improve some known results in the literature.

Quadratic minimization for equilibrium problem variational inclusion and fixed point problem

The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results.