scholarly journals About One Class of Operators Inclusions

2015 ◽  
Vol 19 (3) ◽  
pp. 63-72
Author(s):  
N. A. Demyankov ◽  
V. S. Klimov
Keyword(s):  
Variational Inequalities ◽  
Bounded Operator ◽  
Multivalued Mappings ◽  
Homotopy Invariance ◽  
Operator Inclusion ◽  
Reflexive Space ◽  
Multivalued Operators ◽  
Set Up ◽  
Monotone Type

The operator inclusion 0 ∈ A(x)+N(x) is studied. The main results refer to the case, when A – a bounded operator of monotone type from a reflexive space into conjugate to it, N – a conevalued operator. No solution criterion of the viewed inclusion is set up. Integer characteristics of multivalued mappings with homotopy invariance and additivity are introduced. Application to the theory of variational inequalities with multivalued operators is identified.

scholarly journals Existence results for double phase implicit obstacle problems involving multivalued operators

2020 ◽  
Vol 59 (5) ◽  
Author(s):  
Shengda Zeng ◽  
Yunru Bai ◽  
Leszek Gasiński ◽  
Patrick Winkert
Keyword(s):  
Nonsmooth Analysis ◽  
Existence Results ◽  
Obstacle Problems ◽  
Multivalued Mappings ◽  
Phase Operator ◽  
Generalized Gradient ◽  
Double Phase ◽  
Fixed Point Principle ◽  
Multivalued Operators ◽  
Gradient Based

Abstract In this paper we study implicit obstacle problems driven by a nonhomogenous differential operator, called double phase operator, and a multivalued term which is described by Clarke’s generalized gradient. Based on a surjectivity theorem for multivalued mappings, Kluge’s fixed point principle and tools from nonsmooth analysis, we prove the existence of at least one solution.

scholarly journals Evolutionary quasi-variational and variational inequalities with constraints on the derivatives

2018 ◽  
Vol 9 (1) ◽  
pp. 250-277 ◽  
Author(s):  
Fernando Miranda ◽  
José Francisco Rodrigues ◽  
Lisa Santos
Keyword(s):  
Variational Inequalities ◽  
General Framework ◽  
Convex Sets ◽  
Nonlinear Evolution ◽  
Strong Solutions ◽  
Linear Operators ◽  
Variational Solutions ◽  
Derivatives Of ◽  
Monotone Type ◽  
Evolution Systems

Abstract This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasi-linear operators are of monotone type, but are not required to be coercive for the existence of weak solutions, which is obtained by a double penalization/regularization for the approximation of the solutions. In the case of time-dependent convex sets that are independent of the solution, we show also the uniqueness and the continuous dependence of the strong solutions of the variational inequalities, extending previous results to a more general framework.

scholarly journals Fixed Point Results for Multivalued Contractive Mappings Endowed with Graphic Structure

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib ◽  
Badriah A. S. Alamri ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
Contractive Mappings ◽  
Set Up

The aim of this paper is to introduce the notion of admissible multivalued mappings and to set up fixed point results for such mappings fulfilling generalized locally Ćirić type rational-contractive conditions on a closed ball in complete dislocated b-metric space. Example and application have been given to demonstrate the novelty of our results. Our results combine, extend, and infer several comparable results in the existing literature.

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