Alternative Theorems for Nonlinear
نویسندگان
چکیده
This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of several special cases such as nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems, and then two suucient existence conditions, are established for this class of nonlinear projection equations. We use one of the alternative theorems to establish several new existence results for generalized complementarity problems with new classes of functions such as quasi-P , and P(; ;)-maps. The class of quasi-P-maps is broad enough to encompass the union of quasi-monotone maps and nonlinear P-maps. The existence results established here signiicantly relax several previous solution conditions in the literature.
منابع مشابه
Random fixed point theorems with an application to a random nonlinear integral equation
In this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. We discuss also the existence of a solution to a nonlinear random integral equation in Banah spaces.
متن کاملAlternative Theorems for Nonlinear Projection
This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems are established for this class of nonlinear projection equations. We utilize one of the alternative theorems to establish several ne...
متن کاملSolving infinite system of nonlinear integral equations by using F-generalized Meir-Keeler condensing operators, measure of noncompactness and modified homotopy perturbation.
In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...
متن کاملCoupled coincidence point and common coupled fixed point theorems in complex valued metric spaces
In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illus...
متن کاملFixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$ in the set...
متن کامل