Fredholm alternative for nonlinear k-ball-contractive mappings with applications

Common fixed point theorems for generalized contractive mappings with applications

Certain common fixed point results involving four mappings satisfying generalized contractive conditions on a cone metric type space are obtained. Our results substantially improve and extend a number of known results. An example is given in support of the new results developed here. As an application, we establish the existence of a solution for an implicit integral equation. MSC: Primary 47H0...

On the Fredholm Alternative for Nonlinear Operators

Let X be a locally convex topological vector space, Y a real Banach space, ƒ a mapping (in general, nonlinear) of X into Y. In several recent papers ([5], [ó], [7]), Pohozaev has studied the concept of normal solvability or the Fredholm alternative for mappings ƒ of class C. If Ax=f'x' is the continuous linear mapping of X into Y which is the derivative of ƒ a t the point x of X, A* the adjoint...

Common Fixed-point Theorems for Nonlinear Weakly Contractive Mappings

The Banach contraction principle is one of the pivotal results in the metric fixed-point theory. It is a popular tool for the solution of existence problems in various fields of mathematics. There are several generalizations of the Banach contraction principle in the related literature on the metric fixed-point theory. Ran and Reurings [15] extended the Banach contraction principle in partially...

Some Results for Cyclic Nonlinear Contractive Mappings in Metric Spaces

In this paper, the concept of cyclic (φ− ψ)-Kannan and cyclic (φ− ψ)-Chatterjea contractions, and fixed point theorems for these types of mappings in the context of complete metric spaces have been introduced. The results proved here extend some fixed point theorems in the literature.

Some Fixed Point Theorems for Nonlinear Set-Valued Contractive Mappings