Fixed point theorems for nonexpansive operators with dissipative perturbations in cones (original) (raw)

Fixed point methods and accretivity for perturbed nonlinear equations in Banach spaces

Journal of Mathematical Analysis and Applications, 2020

In this paper we use fixed point theorems to guarantee the existence of solutions for inclusions of the form Au + λu + F u g, where A is a quasi-m-accretive operator defined in a Banach space, λ > 0, and the nonlinear perturbation F satisfies some suitable conditions. We apply the obtained results, among other things, to guarantee the existence of solutions of boundary value problems of the type −Δρ(u(x)) + λu(x) + F u(x) = g(x), x ∈ Ω, and ρ(u) = 0 on ∂Ω, where the Laplace operator Δ should be understood in the sense of distributions over Ω and to study the existence and uniqueness of solution for a nonlinear integro-differential equation posed in L 1 (Ω).

Fixed point theorems for a system of operator equations with applications

2016

The purpose of this paper is to present some existence and uniqueness theorems for a general system of operator equations. The abstract result generalizes some existence results obtained in [V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 7347-7355] for the case of coupled fixed point problem. We also provide an application to a system of integro-differential equations.

Nonlinear equations involving m-accretive operators

Journal of Mathematical Analysis and Applications, 1983

Let X be a Banach space and T an m-accretive operator defined on a subset D(T) of X and taking values in 2'. For the class of spaces whose bounded closed and convex subsets have the fixed point property for nonexpansive self-mappings, it is shown here that two boundary conditions which imply existence of zeroes for T, appear to be equivalent. This fact is then used to prove that if there exists x,, E D(T) and a bounded open neighborhood U of x0, such that / T(x,)j < r ,< j T(x)1 for all x E &!Jn D(T), then the open ball B(0; r) is contained in the range of T.

Existence of fixed points for condensing operators under an integral condition

Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania and M. Aliaskaria which are generalization of Darbo's fixed point theorem. As application we use these results to solve an integral equations in Banach spaces.

Convergence Results for Fixed Point Problems of Accretive Operators in Banach Spaces

2020

This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach space. A weak convergence of a three - step iterative scheme involving the resolvents of accretive operators is proved. The main result is applied to a convex minimization problem in Hilbert spaces. In particular, the minimizer of a convex and proper lower semi-continuous function defined in a Hilbert space was obtained. Numerical illustration with graphical display of the convergence of the sequence obtained from the iterative scheme is also presented.

On a fixed point theorem in Banach algebras with applications

Applied Mathematics Letters, 2005

In this article it is shown that some of the hypotheses of a fixed point theorem of the present author [B.C. Dhage, On some variants of Schauder's fixed point principle and applications to nonlinear integral equations, J. Math. Phys. Sci. 25 (1988) 603-611] involving two operators in a Banach algebra are redundant. Our claim is also illustrated with the applications to some nonlinear functional integral equations for proving the existence results.

Existence, well-posedness of coupled fixed points and application to nonlinear integral equations

2021

We investigate a fixed point problem for coupled Geraghty type contraction in a metric space with a binary relation. The role of the binary relation is to restrict the scope of the contraction to smaller number of ordered pairs. Such possibilities have been explored for different types of contractions in recent times which has led to the emergence of relational fixed point theory. Geraghty type contractions arose in the literatures as a part of research seeking the replacement contraction constants by appropriate functions. Also coupled fixed point problems have evoked much interest in recent times. Combining the above trends we formulate and solve the fixed point problem mentioned above. Further we show that with some additional conditions such solution is unique. Well-posedness of the problem is investigated. An illustrative example is discussed. The consequences of the results are discussed considering α-dominated mappings and graphs on the metric space. Finally we apply our resu...

Fixed point theorems for Φp operator in cone Banach spaces

Fixed Point Theory and Applications, 2013

In this paper a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm x C = d(x, 0), if there exist a, b, c, r and T : C → C satisfies the conditions 0 ≤ q (r) < q (a) + 2(q (b) + q (c)) and a p (d(Tx, Ty)) + b p (d(x, Tx)) + c p (d(y, Ty)) ≤ r p (d(x, y)) for all x, y ∈ C, then T has at least one fixed point. MSC: 47H10; 54H25