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1. CMB Online first
Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces In this paper, we investigate the common
approximate fixed point sequences of nonexpansive semigroups of
nonlinear mappings $\{T_t\}_{t \geq 0}$, i.e., a family such that
$T_0(x)=x$, $T_{s+t}=T_s(T_t(x))$, where the domain is a metric space
$(M,d)$. In particular we prove that under suitable conditions, the
common approximate fixed point sequences set is the same as the common
approximate fixed point sequences set of two mappings from the family.
Then we use the Ishikawa iteration to construct a common approximate
fixed point sequence of nonexpansive semigroups of nonlinear
mappings.
Keywords:approximate fixed point, fixed point, hyperbolic metric space, Ishikawa iterations, nonexpansive mapping, semigroup of mappings, uniformly convex hyperbolic space Categories:47H09, 46B20, 47H10, 47E10 |
2. CMB 2011 (vol 55 pp. 214)
Positive Solutions of Impulsive Dynamic System on Time Scales In this paper, some criteria for the existence of positive solutions of a class
of systems of impulsive dynamic equations on time scales are obtained by
using a fixed point theorem in cones.
Keywords:time scale, positive solution, fixed point, impulsive dynamic equation Categories:39A10, 34B15 |
3. CMB 2011 (vol 56 pp. 80)
Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity |
Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity In this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's
and Schaefer's fixed point theorems are employed in the analysis.
The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions.
We employ Liapunov's direct method to obtain such an a priori bound.
In the process, we compare these theorems in terms of assumptions and outcomes.
Keywords:Volterra integral equation, periodic solutions, Liapunov's method, Krasnosel'skii's fixed point theorem, Schaefer's fixed point theorem Categories:45D05, 45J05 |
4. CMB 2011 (vol 54 pp. 464)
A Characterization of the Compound-Exponential Type Distributions In this paper, a fixed point equation of the
compound-exponential type distributions is derived, and under some
regular conditions,
both the existence and uniqueness of
this fixed point equation are investigated.
A question posed by Pitman and Yor
can be partially answered by using our approach.
Keywords:fixed point equation, compound-exponential type distributions Categories:62E10, 60G50 |
5. CMB 2011 (vol 55 pp. 15)
Browder's Convergence for One-Parameter Nonexpansive Semigroups We give the sufficient and necessary conditions
of Browder's convergence theorem
for one-parameter nonexpansive semigroups
which was proved by Suzuki.
We also discuss the perfect kernels of topological spaces.
Keywords:nonexpansive semigroup, common fixed point, Browder's convergence, perfect kernel Category:47H20 |
6. CMB 2008 (vol 51 pp. 217)
A Multivalued Nonlinear System with the Vector $p$-Laplacian on the Semi-Infinity Interval We study a second order nonlinear system driven by the vector
$p$-Laplacian, with a multivalued nonlinearity and defined on
the positive time semi-axis $\mathbb{R}_+.$ Using degree
theoretic techniques we solve an auxiliary mixed boundary value
problem defined on the finite interval $[0,n]$ and then via a
diagonalization method we produce a solution for the original
infinite time-horizon system.
Keywords:semi-infinity interval, vector $p$-Laplacian, multivalued nonlinear, fixed point index, Hartman condition, completely continuous map Category:34A60 |
7. CMB 2000 (vol 43 pp. 294)
Fixed Points of Commuting Holomorphic Maps Without Boundary Regularity We identify a class of domains of $\C^n$ in which any two commuting
holomorphic self-maps have a common fixed point.
Keywords:Holomorphic self-maps, commuting functions, fixed points, Wolff point, Julia's Lemma Categories:32A10, 32A40, 32H15, 32A30 |