scholarly journals Nonlinear mappings of monotone type in Banach spaces

1972 ◽  
Vol 11 (3) ◽  
pp. 251-294 ◽  
Author(s):  
Felix E. Browder ◽  
Peter Hess
Keyword(s):  
Banach Spaces ◽  
Monotone Type ◽  
Nonlinear Mappings

scholarly journals Nearly Contraction Mapping Principle for Fixed Points of Hemicontinuous Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Xavier Udo-utun ◽  
M. Y. Balla ◽  
Z. U. Siddiqui
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Nonlinear Mappings

We extend the application of nearly contraction mapping principle introduced by Sahu (2005) for existence of fixed points of demicontinuous mappings to certain hemicontinuous nearly Lipschitzian nonlinear mappings in Banach spaces. We have applied certain results due to Sahu (2005) to obtain conditions for existence—and to introduce an asymptotic iterative process for construction—of fixed points of these hemicontractions with respect to a new auxiliary operator.

scholarly journals On local convexity of nonlinear mappings between Banach spaces

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Iryna Banakh ◽  
Taras Banakh ◽  
Anatolij Plichko ◽  
Anatoliy Prykarpatsky
Keyword(s):  
Banach Space ◽  
Lower Bound ◽  
Banach Spaces ◽  
Lipschitz Constant ◽  
Second Order ◽  
Local Convexity ◽  
Convexity Number ◽  
Locally Convex ◽  
Nonlinear Mappings

AbstractWe find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.

scholarly journals Nonlinear random operator equations and inequalities in Banach spaces

1992 ◽  
Vol 15 (1) ◽  
pp. 111-118 ◽  
Author(s):  
Antonios Karamolegos ◽  
Dimitrios Kravvaritis
Keyword(s):  
Banach Spaces ◽  
Existence Theorems ◽  
Random Operator ◽  
Measurable Selection ◽  
Hammerstein Integral Equation ◽  
Operator Equations ◽  
Deterministic Theory ◽  
Measurable Multifunctions ◽  
Selection Theorems ◽  
Monotone Type

In this paper we give some new existence theorems for nonlinear random equations and inequalities involving operators of monotone type in Banach spaces. A random Hammerstein integral equation is also studied. In order to obtain random solutions we use some results from the existing deterministic theory as well as from the theory of measurable multifunctions and, in particular, the measurable selection theorems of Kuratowski/Ryll-Nardzewski and of Saint-Beuve.

scholarly journals Approximating fixed points of enriched nonexpansive mappings in Banach spaces by using a retraction-displacement condition

2020 ◽  
Vol 36 (1) ◽  
pp. 27-34 ◽  
Author(s):  
VASILE BERINDE
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Displacement Condition ◽  
Nonlinear Mappings

In this paper, we prove convergence theorems for a fixed point iterative algorithm of Krasnoselskij-Mann typeassociated to the class of enriched nonexpansive mappings in Banach spaces. The results are direct generaliza-tions of the corresponding ones in [Berinde, V.,Approximating fixed points of enriched nonexpansive mappings byKrasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35 (2019), No. 3, 293–304.], from the setting of Hilbertspaces to Banach spaces, and also of some results in [Senter, H. F. and Dotson, Jr., W. G.,Approximating fixed pointsof nonexpansive mappings, Proc. Amer. Math. Soc.,44(1974), No. 2, 375–380.], [Browder, F. E., Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197–228.], byconsidering enriched nonexpansive mappings instead of nonexpansive mappings. Many other related resultsin literature can be obtained as particular instances of our results.

Sign in / Sign up

Export Citation Format

Share Document