• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.839-853
• /
• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• East Asian mathematical journal
• /
• v.28 no.5
• /
• pp.597-604
• /
• 2012

Let C be a nonempty closed convex subset of real Hilbert space H and F = $\{S(t):t{\geq}0\}$ a nonexpansive self-mapping semigroup of C, and $f:C{\rightarrow}C$ is a fixed contractive mapping. Consider the process {$x_n$} : $$\{{x_{n+1}={\beta}_nx_n+(1-{\beta}_n)z_n\\z_n={\alpha}_nf(x_n)+(1-{\alpha}_n)S(t_n)P_C(x_n-r_nAx_n)$$. It is shown that {$x_n$} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

• Communications of the Korean Mathematical Society
• /
• v.9 no.4
• /
• pp.819-823
• /
• 1994

If H is a Hilbert space, then an operator $T : D(T) \subset H \to H$ is said to be monotone if $$ (x-y, Tx-Ty) \geq 0$$ for any x, y in D(T). Many authors [1], [4] obtained the existence theorem for the equation $y = x + Tx$ for x, given an element y in H and a monotone operator T. On the other hand some iterative methods were applied to the approximations for the solution of the above equation [6], [8]. For example Bruck [2] obtained the iterative solution of the above equation with an explicit error estimate as follows.

• Journal of applied mathematics & informatics
• /
• v.34 no.3_4
• /
• pp.309-317
• /
• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• Journal of the Chungcheong Mathematical Society
• /
• v.17 no.1
• /
• pp.77-83
• /
• 2004

The aim of this work is to generalize parametric approximation in order to apply them to an one-sided $L_1$-approximation. A natural question now arises : when is the parameter map $$P:f{\rightarrow}P_{K(f)}(f)$$ continuous on $C_1(X)$ ? We find some results with a monotone decreasing sequence about above question.

• Honam Mathematical Journal
• /
• v.8 no.1
• /
• pp.1-19
• /
• 1986

We show that a (possibly unbounded) linear operator, T, is scalar on the real line (spectral operator of scalar type, with real spectrum) if and only if (iT) generates a uniformly bounded semigroup and $(1-iT)(1+iT)^{-1}$ is scalar on the unit circle. T is scalar on [0, $\infty$) if and only if T generates a uniformly bounded semigroup and $(1+T)^{-1}$ is scalar on [0,1). By analogy with these results, we define $C^0$-scalar, on the real line, or [0. $\infty$), for an unbounded operator. We show that a generator of a positive-definite group is $C^0$-scalar on the real line. and a generator of a completely monotone semigroup is $C^0$-scalar on [0, $\infty$). We give sufficient conditions for a closed operator, T, to generate a positive-definite group: the sequence < $\phi(T^{n}x)$ > $_{n=0}^{\infty}$ must equal the moments of a positive measure on the real line, for sufficiently many positive $\phi$ in $X^{*}$, x in X. If the measures are supported on [0, $\infty$), then T generates a completely monotone semigroup. On a reflexive Banach lattice, these conditions are also necessary, and are equivalent to T being scalar, with positive projection-valued measure. T generates a completely monotone semigroup if and only if T is positive and m-dispersive and generates a bounded holomorphic semigroup.

• The Pure and Applied Mathematics
• /
• v.24 no.2
• /
• pp.79-98
• /
• 2017

We establish a coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X{\times}X{\rightarrow}X$ under generalized symmetric Meir-Keeler contraction on a partially ordered metric space. We also deduce certain coupled fixed point results without mixed monotone property of $F:X{\times}X{\rightarrow}X$. An example supporting to our result has also been cited. As an application the solution of integral equations are obtain here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.23 no.9
• /
• pp.1146-1151
• /
• 2019

Histogram H is an x-monotone rectilinear polygon with a horizontal edge, called by a base, connecting the leftmost vertical edge and the rightmost vertical edge. Here the rectilinear polygon is a polygon with only horizontal and vertical edges and the x- monotone polygon P is a polygon in which every line orthogonal to the x-axis intersects P at most twice. Walking counterclockwise on the boundary of a histogram H yields a sequence of left turns and right turns at its vertices. Conversely, a given sequence of the turns at the vertices can be realized by a histogram. In this paper, we consider the problem of finding a histogram to realize a given turn sequence. Particularly, we will find the histograms to minimize its area and its bounding box. It will be shown that both of the problems can be solved by linear time algorithms.

• Bulletin of the Korean Mathematical Society
• /
• v.30 no.2
• /
• pp.179-185
• /
• 1993

In this article S is a topologically complete subspace of $R^{1}$i.e., the relativized topology on S may be metrized so as to make S complete. B(S) is the Borel .sigma.-field of S. For .GAMMA. one takes a set of measurable monotone (increasing or dereasing) functions on S into itself. Make the assumption of pp. There exists $x_{0}$ and a positive integer $n_{0}$ such that (Fig.) It is then shown that there exists a unique inveriant probability to which $p^{(n)}$ (x,dy) converges exponentially fast in a metric (stronger than the Kolmogorov distance); this convergence is uniform for all x .mem. S. This generalizes an earlier result of Bhattacharya and Lee (1988) who considered monotone nondecreasing maps on S.

• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.73-96
• /
• 2016

We establish a coupled coincidence point theorem for generalized com-patible pair of mappings under generalized nonlinear contraction on a partially or-dered metric space. We also deduce certain coupled fixed point results without mixed monotone property of F : X × X → X . An example supporting to our result has also been cited. As an application the solution of integral equations are obtained here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.