scholarly journals On the Rockafellar function associated to a non-cyclically monotone mapping

2019 ◽  
Vol 64 (3) ◽  
pp. 413-420
Author(s):  
Teodor Precupanu ◽  
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Keyword(s):  
Monotone Mapping

scholarly journals Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Tanom Chamnarnpan ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Monotone Mapping ◽  
Iterative Algorithms ◽  
Infinite Family ◽  
Common Element ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for aβ-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

Biconnected Multifunctions of Trees which have an end Point as Fixed Point or Coincidence

1971 ◽  
Vol 23 (3) ◽  
pp. 461-467 ◽  
Author(s):  
Helga Schirmer
Keyword(s):  
Fixed Point ◽  
Monotone Mapping ◽  
Monotone Mappings ◽  
Point Sets ◽  
End Point ◽  
Continuous Use ◽  
Fixed Point Sets

It was proved almost forty years ago that every mapping of a tree into itself has at least one fixed point, but not much is known so far about the structure of the possible fixed point sets. One topic related to this question, the study of homeomorphisms and monotone mappings of trees which leave an end point fixed, was first considered by G. E. Schweigert [6] and continued by L. E. Ward, Jr. [8] and others. One result by Schweigert and Ward is the following: any monotone mapping of a tree onto itself which leaves an end point fixed, also leaves at least one other point fixed.It is further known that not only single-valued mappings, but also upper semi-continuous (use) and connected-valued multifunctions of trees have a fixed point [7], and that two use and biconnected multifunctions from one tree onto another have a coincidence [5].

scholarly journals Relaxed Inertial Tseng’s Type Method for Solving the Inclusion Problem with Application to Image Restoration

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 818 ◽  
Author(s):  
Jamilu Abubakar ◽  
Poom Kumam ◽  
Abdulkarim Hassan Ibrahim ◽  
Anantachai Padcharoen
Keyword(s):  
Lipschitz Constant ◽  
Monotone Mapping ◽  
Splitting Method ◽  
Split Feasibility Problem ◽  
Monotone Operators ◽  
Feasibility Problem ◽  
Inclusion Problem ◽  
Variable Step Size ◽  
Step Size ◽  
Type Method

The relaxed inertial Tseng-type method for solving the inclusion problem involving a maximally monotone mapping and a monotone mapping is proposed in this article. The study modifies the Tseng forward-backward forward splitting method by using both the relaxation parameter, as well as the inertial extrapolation step. The proposed method follows from time explicit discretization of a dynamical system. A weak convergence of the iterates generated by the method involving monotone operators is given. Moreover, the iterative scheme uses a variable step size, which does not depend on the Lipschitz constant of the underlying operator given by a simple updating rule. Furthermore, the proposed algorithm is modified and used to derive a scheme for solving a split feasibility problem. The proposed schemes are used in solving the image deblurring problem to illustrate the applicability of the proposed methods in comparison with the existing state-of-the-art methods.

When a vector quasimonotone mapping is a vector monotone mapping

2014 ◽  
Vol 8 (7) ◽  
pp. 2127-2134
Author(s):  
A. P. Farajzadeh ◽  
S. Plubtieng
Keyword(s):  
Monotone Mapping ◽  
Quasimonotone Mapping
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