Point Theorem For Multivalued Operators Research Articles

Anisotropic and isotropic implicit obstacle problems with nonlocal terms and multivalued boundary conditions

In this paper we study an anisotropic implicit obstacle problem driven by the (p(⋅),q(⋅))-Laplacian and an isotropic implicit obstacle problem involving a nonlinear convection term (a reaction term depending on the gradient) which contain several interesting and challenging untreated problems. These two implicit obstacle problems have both highly nonlinear and nonlocal functions and three multivalued terms where two of them are appearing on the boundary and the other one is formulated in the domain. Under very general assumptions on the data, we develop general frameworks to examine the nonemptiness and compactness of the set of weak solutions to the problems under consideration. The proofs of our main results use the theory of nonsmooth analysis, Tychonoff’s fixed point theorem for multivalued operators, the theory of pseudomonotone operators and variational approach.

Double Phase Implicit Obstacle Problems with Convection and Multivalued Mixed Boundary Value Conditions

In this paper we consider a mixed boundary value problem with a nonhomogeneous, nonlinear differential operator (called double phase operator), a nonlinear convection term (a reaction term depending on the gradient), three multivalued terms and an implicit obstacle constraint. Under very general assumptions on the data, we prove that the solution set of such implicit obstacle problem is nonempty (so there is at least one solution) and weakly compact. The proof of our main result uses the Kakutani-Ky Fan fixed point theorem for multivalued operators along with the theory of nonsmooth analysis and variational methods for pseudomonotone operators.

Fixed Point Results for Multivalued Operators On b_2 Metric Spaces

Bu çalışmanın amacı, 𝑏2 -metrik uzayında çok değişkenli operatörler için sabit nokta teoremi oluşturmak ve Chifu ve Petruşel (2017) ve Yihao, Ren ve Zhong (2018) sonuçlarını genelleştirmektir. Ayrıca, ana teoremi göstermek için bir örnek verilmiştir. Bu çalışmanın amacı, 𝑏2 -metrik uzayında çok değişkenli operatörler için sabit nokta teoremi oluşturmak ve Chifu ve Petruşel (2017) ve Yihao, Ren ve Zhong (2018) sonuçlarını genelleştirmektir. Ayrıca, ana teoremi göstermek için bir örnek verilmiştir.

Existence of a mild solution for a neutral stochastic fractional integro-differential inclusion with a nonlocal condition

This paper mainly concerns the existence of a mild solution for a neutral stochastic fractional integro-differential inclusion of order $1\lt \beta \lt 2$ with a nonlocal con\-dition in a separable Hilbert space. Utilizing the fixed point theorem for multi-valued operators due to O' Regan, we establish an existence result involving a $\beta $-resolvent operator. An illustrative example is provided to show the effectiveness of the established results.

On Reich’s strict fixed point theorem for multi-valued operators in complete metric spaces

On Reich’s strict fixed point theorem for multi-valued operators in complete metric spaces

Existence of the Mild Solution for an Impulsive Nonlocal Neutral Stochastic Fractional Differential Inclusions with Infinite Delay

This paper studies an impulsive nonlocal neutral stochastic fractional integro-differential inclusions with infinite delays in an arbitrary separable Hilbert space X. The sufficient conditions proving the existence of mild solution of the nonlocal stochastic inclusion problem with impulsive conditions are derived by using resolvent operator and fixed point theorem for multi-valued operators due to O’Regan. An example is also presented to illustrate the obtained theory.

Contributions to the fixed point theory of diagonal operators

AbstractIn this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on the weakly Picard operator technique, difference equation techniques, and some fixed point theorems for multi-valued operators. Some applications to differential and integral equations are given. We also present some research directions.

Mild solution for impulsive neutral fractional partial differential inclusions with nonlocal conditions

In the present paper, we study the existence of a mild solution of a fractional order nonlocal differential inclusion with impulsive condition in a Banach space E. We obtain the sufficient condition for the existence of the mild solution by using a fixed point theorem for multi-valued operators due to Dhage and resolvent semigroup theory with approximate techniques.

Existence of the Mild Solution for Impulsive Neutral Stochastic Fractional Integro-Differential Inclusions with Nonlocal Conditions

This paper mainly concerns with the existence of a mild solution for impulsive neutral integro-differential inclusions with nonlocal conditions in a separable Hilbert space. Utilizing fixed point theorem for multi-valued operators due to Dhage, we establish the existence result with resolvent operator and η-norm. An illustrative example is provided to show the effectiveness of the established results.

Fixed points and strict fixed points for multivalued contractions of Reich type on metric spaces endowed with a graph

Abstract The purpose of this paper is to present some strict fixed point theorems for multivalued operators satisfying a Reich-type condition on a metric space endowed with a graph. The well-posedness of the fixed point problem is also studied. MSC:47H10, 54H25.

Solvability of a Class of Integral Inclusions

This paper presents sufficient conditions for the existence of positive solutions for a class of integral inclusions. Our results are obtained via a new fixed point theorem for multivalued operators developed in the paper, in which some nonnegative function is used to describe the cone expansion and compression instead of the classical norm‐type, and lead to new existence principles.

Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions

We discuss existence results of mild solutions for stochastic differential inclusions subject to nonlocal conditions. We provide sufficient conditions in order to obtain a priori bounds on possible solutions of a one-parameter family of problems related to the original one. We, then, rely on fixed point theorems for multivalued operators to prove our main results.

Fixed point theory for multivalued φ-contractions

AbstractThe purpose of this paper is to present a fixed point theory for multivalued φ-contractions using the following concepts: fixed points, strict fixed points, periodic points, strict periodic points, multivalued Picard and weakly Picard operators; data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, limit shadowing property of a multivalued operator, set-to-set operatorial equations and fractal operators. Our results generalize some recent theorems given in Petruşel and Rus (The theory of a metric fixed point theorem for multivalued operators, Proc. Ninth International Conference on Fixed Point Theory and its Applications, Changhua, Taiwan, July 16-22, 2009, 161-175, 2010).2010 Mathematics Subject Classification47H10; 54H25; 47H04; 47H14; 37C50; 37C70

Discontinuous Parabolic Problems with a Nonlocal Initial Condition

We study parabolic differential equations with a discontinuous nonlinearity and subjected to a nonlocal initial condition. We are concerned with the existence of solutions in the weak sense. Our technique is based on the Green's function, integral representation of solutions, the method of upper and lower solutions, and fixed point theorems for multivalued operators.

The Theory of Reich's Fixed Point Theorem for Multivalued Operators

AbstractThe purpose of this paper is to present a theory of Reich's fixed point theorem for multivalued operators in terms of fixed points, strict fixed points, multivalued weakly Picard operators, multivalued Picard operators, data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, and the generated fractal operator.

Existence results for impulsive neutral stochastic functional integro-differential inclusions with nonlocal initial conditions

In this paper, we prove the existence of mild solutions for a class of impulsive neutral stochastic functional integro-differential inclusions with nonlocal initial conditions and resolvent operators. Sufficient conditions for the existence are derived with the help of the fixed point theorem for multi-valued operators due to Dhage and the fractional power of operators. An example is provided to illustrate the theory.

A FIXED POINT THEOREM FOR MULTI-VALUED WEAKLY PICARD OPERATORS IN b-METRIC SPACE

In this paper, we establish a fixed point theorem for multi-valued operators in a complete b−metric space using the concept of Berinde and Berinde [9] on multi-valued weak contractions for the Picard iteration in a metric space. Our main result generalizes, extends and improves some of the recent results of Berinde and Berinde [9] as well as those of Daffer and Kaneko [17] and also unifies several classical results pertainning to single and multi-valued contractive mappings in the literature. AMS Mathematics Subject Classification: 47H06, 47H10.

A fixed point theorem for multi-valued weakly Picard operators in b-metric space

AbstractIn this paper, we establish a fixed point theorem for multi-valued operators in a complete

Fixed point theorems for multivalued operators and application to discontinuous quasilinear BVP's

In this article, we prove an abstract fixed point theorem for increasing multivalued operators in ordered topological spaces, which provides an efficient tool to obtain qualitative results on the solution set of discontinuous quasilinear elliptic boundary value problems. In particular, we are able to show the existence of extremal solutions of such problems.

On random approximation and coincidence point theorems for multivalued operators

On random approximation and coincidence point theorems for multivalued operators