Professor Anthony To-Ming Lau's contributions to the development of Fixed Point Theory and Applications.

Approximation of fixed points for nonexpansive semigroups in Hilbert spaces

In this paper, we propose two new algorithms for finding a common fixed point of a nonexpansive semigroup in Hilbert spaces and prove some strong convergence theorems for nonexpansive semigroups. Our results i...

Authors: Yonghong Yao, Jung Im Kang, Yeol Je Cho and Yeong-Cheng Liou

Strong convergence by the shrinking effect of two half-spaces and applications

This paper provides a new hybrid-type shrinking projection method for strong convergence results in a Hilbert space. The paper continues - by utilizing the proposed hybrid algorithm - with a strong convergence...

Authors: Muhammad Aqeel Ahmad Khan and Hafiz Fukhar-ud-din

Tripled fixed point theorem in fuzzy metric spaces and applications

In this paper we prove an existence and uniqueness theorem for contractive type mappings in fuzzy metric spaces. In order to do that, we consider a slight modification of the concept of a tripled fixed point i...

Authors: A Roldán, J Martínez-Moreno and C Roldán

Best proximity point results in geodesic metric spaces

In this paper, the existence of a best proximity point for relatively u-continuous mappings is proved in geodesic metric spaces. As an application, we discuss the existence of common best proximity points for a f...

Authors: Maryam A Alghamdi, Mohammed A Alghamdi and Naseer Shahzad

On vector matrix game and symmetric dual vector optimization problem

A vector matrix game with more than two skew symmetric matrices, which is an extension of the matrix game, is defined and the symmetric dual problem for a nonlinear vector optimization problem is considered. U...

Authors: Jeong Min Hong, Moon Hee Kim and Gue Myung Lee

Fixed point theorems for a semigroup of generalized asymptotically nonexpansive mappings in CAT(0) spaces

Authors: Withun Phuengrattana and Suthep Suantai

New complexity analysis for primal-dual interior-point methods for self-scaled optimization problems

A linear optimization problem over a symmetric cone, defined in a Euclidean Jordan algebra and called a self-scaled optimization problem (SOP), is considered. We formulate an algorithm for a large-update prima...

Authors: Bo Kyung Choi and Gue Myung Lee

Best proximity point theorems for reckoning optimal approximate solutions

Given a non-self mapping from A to B, where A and B are subsets of a metric space, in order to compute an optimal approximate solution of the equation

Authors: S Sadiq Basha, N Shahzad and R Jeyaraj

Boundary value problem of a nonlinear Langevin equation with two different fractional orders and impulses

In this paper, we study a new type of a Langevin equation involving two different fractional orders and impulses. Sufficient conditions are formulated for the existence and uniqueness of solutions of the given...

Authors: Guotao Wang, Lihong Zhang and Guangxing Song

Uniform mean convergence theorems for hybrid mappings in Hilbert spaces

Using the notion of sequences of means on the Banach space of all bounded real sequences, we prove mean and uniform mean convergence theorems for pointwise convergent sequences of hybrid mappings in Hilbert sp...

Authors: Koji Aoyama and Fumiaki Kohsaka

Some new properties of the Lagrange function and its applications

Using a dual problem in Wolfe type, the Lagrange function of an inequality constrained nonconvex programming problem is proved to be constant not only on its optimal solution set but also on a wider set. In ad...

Authors: Do Sang Kim and Ta Quang Son

Strong convergence of a proximal-type algorithm for an occasionally pseudomonotone operator in Banach spaces

It is known that the proximal point algorithm converges weakly to a zero of a maximal monotone operator, but it fails to converge strongly. Then, in (Math. Program. 87:189-202, 2000), Solodov and Svaiter intro...

Authors: Hemant Kumar Pathak and Yeol Je Cho

Convergence to common solutions of various problems for nonexpansive mappings in Hilbert spaces

In this paper, motivated and inspired by Ceng and Yao (J. Comput. Appl. Math. 214(1):186-201, 2008), Iiduka and Takahashi (Nonlinear Anal. 61(3):341-350, 2005), Jaiboon and Kumam (Nonlinear Anal. 73(5):1180-12...

Authors: Kyung Soo Kim

Iterative methods for mixed equilibrium problems and strictly pseudocontractive mappings

In this paper, we introduce new implicit and explicit iterative schemes for finding a common element of the set of solutions of the mixed equilibrium problem and the set of fixed points of a k-strictly pseudocont...

Authors: Jong Soo Jung

Interior fixed points of unit-sphere-preserving Euclidean maps

Schirmer proved that there is a class of smooth self-maps of the unit sphere in Euclidean n-space with the property that any smooth self-map of the unit ball that extends a map of that class must have at least on...

Authors: Nirattaya Khamsemanan, Robert F Brown, Catherine Lee and Sompong Dhompongsa

Iterative common solutions for monotone inclusion problems, fixed point problems and equilibrium problems

Authors: Wataru Takahashi, Ngai-Ching Wong and Jen-Chih Yao

Implicit eigenvalue problems for maximal monotone operators

We study the implicit eigenvalue problem of the form

Authors: In-Sook Kim

Fixed point solutions of variational inequalities for a semigroup of asymptotically nonexpansive mappings in Banach spaces

The purpose of this article is to introduce two iterative algorithms for finding a common fixed point of a semigroup of asymptotically nonexpansive mappings which is a unique solution of some variational inequ...

Authors: Pongsakorn Sunthrayuth and Poom Kumam

Coupled fixed point theorems for generalized contractive mappings in partially ordered G-metric spaces

In this paper, we establish some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings having the mixed monotone property in partially ordered G-metric spaces. The results...

Authors: Rabian Wangkeeree and Thanatporn Bantaojai

Common fixed-point results in uniformly convex Banach spaces

Authors: Naknimit Akkasriworn, Annop Kaewkhao, Attapol Keawkhao and Kritsana Sokhuma

Regularization method for Noor’s variational inequality problem induced by a hemicontinuous monotone operator

In this paper, we provide a regularization method for finding a solution of Noor’s variational inequality problem induced by a hemicontinuous monotone operator. Moreover, such a solution is related to the set ...

Authors: Yeol Je Cho and Narin Petrot

An improved method for solving multiple-sets split feasibility problem

The multiple-sets split feasibility problem (MSSFP) has a variety of applications in the real world such as medical care, image reconstruction and signal processing. Censor et al. proposed solving the MSSFP by a ...

Authors: Yunfei Du and Rudong Chen

Fixed point results for cyclic $(\psi ,\varphi ,A,B)$-contraction in partial metric spaces

Very recently, Agarwal et al. (Fixed Point Theory Appl. 2012:40, 2012) initiated the study of fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric sp...

Authors: Wasfi Shatanawi and Saurabh Manro

Projection methods of iterative solutions in Hilbert spaces

In this paper, zero points of the sum of two monotone mappings, solutions of a monotone variational inequality, and fixed points of a nonexpansive mapping are investigated based on a hybrid projection iterativ...

Authors: Feng Gu and Jing Lu

Banach contraction principle for cyclical mappings on partial metric spaces

We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilić

Authors: T Abdeljawad, JO Alzabut, A Mukheimer and Y Zaidan

Total quasi-ϕ-asymptotically nonexpansive semigroups and strong convergence theorems in Banach spaces

The purpose of this article is to modify the Halpern-Mann-type iteration algorithm for total quasi-ϕ-asymptotically nonexpansive semigroups to have the strong convergence under a limit condition only in the frame...

Authors: Shih-sen Chang, Jong Kyu Kim and Lin Wang

Split feasibility problems for total quasi-asymptotically nonexpansive mappings

The purpose of this paper is to propose an algorithm for solving the split feasibility problems for total quasi-asymptotically nonexpansive mappings in infinite-dimensional Hilbert spaces. The results presented i...

Authors: Xiong Rui Wang, Shih-sen Chang, Lin Wang and Yun-he Zhao

Nonexpansive mappings on Abelian Banach algebras and their fixed points

Authors: W Fupinwong

A three-step iterative scheme for solving nonlinear ϕ-strongly accretive operator equations in Banach spaces

In this paper, we study a three-step iterative scheme with error terms for solving nonlinear ϕ-strongly accretive operator equations in arbitrary real Banach spaces.

Authors: Safeer Hussain Khan, Arif Rafiq and Nawab Hussain

Some results on fixed points of asymptotically strict quasi-ϕ-pseudocontractions in the intermediate sense

In this paper, a new nonlinear mapping, asymptotically strict quasi-ϕ-pseudocontraction in the intermediate sense, is introduced. Projection algorithms are considered for the mapping. Strong convergence theorems ...

Authors: Xiaolong Qin, Lin Wang and Shin Min Kang

Some connections between the attractors of an IIFS $\mathcal{S}$ and the attractors of the sub-IFSs of $\mathcal{S}$

Based on the results from (Mihail and Miculescu in Math. Rep., Bucur. 11(61)(1):21-32, 2009), where the shift space for an infinite iterated function system (IIFS for short) is defined and the relation between...

Authors: Radu Miculescu and Loredana Ioana

Common fixed points of Ćirić-type contractive mappings in two ordered generalized metric spaces

In this paper, using the setting of two ordered generalized metric spaces, a unique common fixed point of four mappings satisfying a generalized contractive condition is obtained. We also present an example to...

Authors: M Abbas, YJ Cho and T Nazir

Strong convergence theorems for fixed points of asymptotically strict quasi-ϕ-pseudocontractions

In this paper, the fixed point problem of asymptotically strict quasi-ϕ-pseudocontractions is investigated based on hybrid projection algorithms. Strong convergence theorems of fixed points are established in a r...

Authors: Qing-Nian Zhang

Strong convergence theorems for a common point of solution of variational inequality, solutions of equilibrium and fixed point problems

We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for continuous monotone mapping, solution of equilibrium problem and a common fixed po...

Authors: Habtu Zegeye, Naseer Shahzad and Mohammad Ali Alghamdi

Common fixed points for some generalized nonexpansive mappings and nonspreading-type mappings in uniformly convex Banach spaces

In this article, we study the fixed point theorems for nonspreading mappings, defined by Kohsaka and Takahashi, in Banach spaces but using the sense of norm instead of using the function ϕ. Furthermore, we prove ...

Authors: Warunun Inthakon, Attapol Kaewkhao and Nutchari Niyamosot

An approximation method for common fixed points of a finite family of asymptotic pointwise nonexpansive mappings

In this article, we consider an iterative scheme to approximate a common fixed point for a finite family of asymptotic pointwise nonexpansive mappings. We obtain weak and strong convergence theorems of the pro...

Authors: Bancha Nanjaras and Bancha Panyanak

On a hybrid algorithm for a family of total quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces

The purpose of this article is to introduce the concept of total quasi- ϕ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and we prove a strong convergence theorem b...

Authors: Ping Zuo, Shih-sen Chang and Min Liu