Articles

Common fixed point theorems of integral type contraction on metric spaces and its applications to system of functional equations

Authors: Muhammad Sarwar, Mian Bahadur Zada and İnci M Erhan

Metric fixed point theory: a brief retrospective

These remarks are based on a talk the writer gave at the 11th International Conference in Fixed Point Theory and Applications, held at Galatasaray University in Istanbul, Turkey, July 20-24, 2015. They represe...

Authors: William A Kirk

Non-convex hybrid algorithm for a family of countable quasi-Lipschitz mappings and application

The purpose of this article is to establish a kind of non-convex hybrid iteration algorithms and to prove relevant strong convergence theorems of common fixed points for a uniformly closed asymptotically famil...

Authors: Jinyu Guan, Yanxia Tang, Pengcheng Ma, Yongchun Xu and Yongfu Su

Strong convergence theorem for totally quasi-ϕ-asymptotically nonexpansive multi-valued mappings under relaxed conditions

We construct a relaxed hybrid shrinking iteration algorithm for approximating common fixed points of a countable family of totally quasi-ϕ-asymptotically nonexpansive multi-valued mappings. A strong convergence t...

Authors: Shanguang Qian

Strong convergence theorems for asymptotically nonexpansive nonself-mappings with applications

In this paper, first, we introduce the condition (BP) which is weaker than the completely continuous mapping in Banach spaces. Second, we consider a simple iteration and prove some strong convergence theorems ...

Authors: Weiping Guo, Afrah AN Abdou, Liaqat A Khan and Yeol Je Cho

Inductive properties of fixed point sets of mappings on posets and on partially ordered topological spaces

In this paper, we prove several fixed point theorems on both posets and partially ordered topological spaces for set-valued mappings. We also provide the inductive properties of the sets of fixed points for so...

Authors: Jinlu Li

Fixed point theorems for Meir-Keeler type mappings in M-metric spaces with applications

In this paper, we establish some fixed point theorems for a Meir-Keeler type contraction in M-metric spaces via Gupta-Saxena type contraction. Also, we extend and improve very recent results in fixed point theory...

Authors: Mehdi Asadi

Some fixed point results for non-decreasing and mixed monotone mappings with auxiliary functions

The purpose of this paper is to provide sufficient conditions for the existence and uniqueness of fixed points for non-decreasing and mixed monotone mappings with auxiliary functions in the framework of metric...

Authors: Shuang Wang, Arslan Hojat Ansari and Sumit Chandok

Split equality fixed point problem for quasi-pseudo-contractive mappings with applications

In this paper, we consider a split equality fixed point problem for quasi-pseudo-contractive mappings which includes split feasibility problem, split equality problem, split fixed point problem etc., as special c...

Authors: Shih-sen Chang, Lin Wang and Li-Juan Qin

Existence of best proximity points for controlled proximal contraction

In this paper, we investigate the sufficient condition for the existence of best proximity points for non-self-multivalued mappings. Additionally, we discuss the stability theorem for such mappings. Our result...

Authors: Quanita Kiran, Muhammad Usman Ali, Tayyab Kamran and Erdal Karapınar

An intermixed algorithm for strict pseudo-contractions in Hilbert spaces

An intermixed algorithm for two strict pseudo-contractions in Hilbert spaces have been presented. It is shown that the suggested algorithms converge strongly to the fixed points of two strict pseudo-contractio...

Authors: Zhangsong Yao, Shin Min Kang and Hong-Jun Li

Self-adaptive algorithms for proximal split feasibility problems and strong convergence analysis

The purpose of the paper is to study the proximal split feasibility problems. For solving the problems, we present new self-adaptive algorithms with the regularization technique. By using these algorithms, we ...

Authors: Yonghong Yao, Zhangsong Yao, Afrah AN Abdou and Yeol Je Cho

Fixed point theorems on cone 2-metric spaces over Banach algebras and an application

In this paper, the concept of cone 2-metric spaces over Banach algebras is introduced and some existence and uniqueness theorems of fixed points for some mappings satisfying certain contractive conditions are ...

Authors: Tao Wang, Jiandong Yin and Qi Yan

Erratum to: An implicit method for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces

Authors: Nawab Hussain, Mahmood Lashkarizadeh Bami and Ebrahim Soori

General iterative methods for monotone mappings and pseudocontractive mappings related to optimization problems

In this paper, we introduce two general iterative methods for a certain optimization problem of which the constrained set is the common set of the solution set of the variational inequality problem for a conti...

Authors: Jong Soo Jung

New result on fixed point theorems for φ-contractions in Menger spaces

Very recently, Fang (Fuzzy Sets Syst. 267:86-99, 2015) gave some fixed point theorems for probabilistic φ-contractions in Menger spaces. Fang’s results improve the one of Jachymski (Nonlinear Anal. 73:2199-2203, ...

Authors: Huichun Hua, Minjiang Chen and Shenghua Wang

Shrinking projection methods for solving split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings in Hilbert spaces

In this paper, we propose a new iterative sequence for solving common problems which consist of split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings in the framework of ...

Authors: Uamporn Witthayarat, Afrah A N Abdou and Yeol Je Cho

Common endpoints of generalized weak contractive mappings via separation theorem with applications

In this paper, first, we give the separation theorem which is an extension of the separation theorem due to Jachymski and Jóźwik (J. Math. Anal. Appl. 300:147-159, 2004). Then, by using this and the related re...

Authors: Sirous Moradi, Ali P Farajzadeh, Yeol Je Cho and Somyot Plubtieng

Sharpening some core theorems of Nieto and Rodríguez-López with application to boundary value problem

In this paper, we prove sharpened versions of some classical order-theoretic metrical fixed point theorems due to Nieto and Rodríguez-López (Order 22(3):223-239, 2005) using order-theoretic variants of complet...

Authors: Marwan Amin Kutbi, Aftab Alam and Mohammad Imdad

Viscosity approximation method for generalized asymptotically quasi-nonexpansive mappings in a convex metric space

A general viscosity iterative method for a finite family of generalized asymptotically quasi-nonexpansive mappings in a convex metric space is introduced. Special cases of the new iterative method are the visc...

Authors: Abdul Rahim Khan, Nusrat Yasmin, Hafiz Fukhar-ud-din and Sami Atif Shukri

Genericity and porosity in fixed point theory: a survey of recent results

We survey recent results regarding genericity and porosity in fixed point theory. These results concern, inter alia, infinite products, nonexpansive mappings, approximate fixed points, contractive mappings, bound...

Authors: Simeon Reich and Alexander J Zaslavski

A topological degree for operators of generalized \((S_{+})\) type

As an extension of the Leray-Schauder degree, we introduce a topological degree theory for a class of demicontinuous operators of generalized

Authors: In-Sook Kim and Suk-Joon Hong

Existence of solutions for a class of operator equations

In this paper we deal with the existence and multiplicity of nontrivial solutions to a class of operator equation. By using infinite dimensional Morse theory, we establish some conditions which guarantee that ...

Authors: Xiaojing Feng

Extra-gradient methods for solving split feasibility and fixed point problems

The purpose of this paper is to study the extra-gradient methods for solving split feasibility and fixed point problems involved in pseudo-contractive mappings in real Hilbert spaces. We propose an Ishikawa-ty...

Authors: Jin-Zuo Chen, Lu-Chuan Ceng, Yang-Qing Qiu and Zhao-Rong Kong

Generalized proximal-type methods for weak vector variational inequality problems in Banach spaces

In this paper, we propose a class of generalized proximal-type method by the virtue of Bregman functions to solve weak vector variational inequality problems in Banach spaces. We carry out a convergence analys...

Authors: Lin-chang Pu, Xue-ying Wang and Zhe Chen

The generalized viscosity implicit rules of nonexpansive mappings in Hilbert spaces

The generalized viscosity implicit rules of nonexpansive mappings in Hilbert spaces are established. The strong convergence theorems of the rules are proved under certain assumptions imposed on the sequences o...

Authors: Yifen Ke and Changfeng Ma

A note on fixed point theory for cyclic φ-contractions

In this paper, we consider, discuss, improve, and complement recent fixed points results for mappings satisfying cyclical contractive conditions established by Pacurar and Rus (Nonlinear Anal. 72:1181-1187, 20...

Authors: Stojan Radenović

Multidimensional common fixed point theorems under probabilistic φ-contractive conditions in multidimensional Menger probabilistic metric spaces

Authors: Chuanxi Zhu, Zhe Wei, Zhaoqi Wu and Wenqing Xu

On Browder’s convergence theorem and Halpern iteration process for G-nonexpansive mappings in Hilbert spaces endowed with graphs

In this paper, we prove Browder’s convergence theorem for G-nonexpansive mappings in a Hilbert space with a directed graph. Moreover, we also prove strong convergence of the Halpern iteration process to a fixed p...

Authors: Jukrapong Tiammee, Attapol Kaewkhao and Suthep Suantai

On an open problem of Kyung Soo Kim

We prove a convergence theorem of the Mann iteration scheme for a uniformly L-Lipschitzian asymptotically demicontractive mapping in a

Authors: Bancha Panyanak

Some fixed point theorems for generalized contractive mappings in complete metric spaces

We introduce new concepts of generalized contractive and generalized α-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on co...

Authors: Nawab Hussain, Vahid Parvaneh, Bessem Samet and Calogero Vetro

Recent results on the topological fixed point theory of multivalued mappings: a survey

In this survey, we present current results from the topological fixed point theory of multivalued mappings which were obtained by ourselves in the last five years (see Andres and Górniewicz in Fixed Point Theo...

Authors: Jan Andres and Lech Górniewicz

A characterization of Smyth complete quasi-metric spaces via Caristi’s fixed point theorem

We obtain a quasi-metric generalization of Caristi’s fixed point theorem for a kind of complete quasi-metric spaces. With the help of a suitable modification of its proof, we deduce a characterization of Smyth...

Authors: Salvador Romaguera and Pedro Tirado

A fixed point iterative approach to integer programming and its distributed computation

Integer programming is concerned with the determination of an integer or mixed-integer point in a polytope. It is an NP-hard problem and has many applications in economics and management. Although several popu...

Authors: Chuangyin Dang and Yinyu Ye

Projective contractions, generalized metrics, and fixed points

In 1981, Borsík and Doboš studied the aggregation problem for metric spaces. Thus, they characterized those functions that allow one to merge a collection of metrics providing a single metric as a result (Bors...

Authors: Maryam A Alghamdi, Naseer Shahzad and Oscar Valero

Hybrid iterative algorithms for two families of finite maximal monotone mappings

In this paper, we introduce and analyze a new general hybrid iterative algorithm for finding a common element of the set of common zeros of two families of finite maximal monotone mappings, the set of fixed po...

Authors: Yang-Qing Qiu, Lu-Chuan Ceng, Jin-Zuo Chen and Hui-Ying Hu

On fixed point theory in topological posets, extended quasi-metric spaces and an application to asymptotic complexity of algorithms

In this paper we present a few fixed point results in the framework of topological posets. To this end, we introduce an appropriate notion of completeness and order-continuity. Special attention is paid to the...

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

Iterative methods for solving the multiple-sets split feasibility problem with splitting self-adaptive step size

We introduce an iterative algorithm for solving the multiple-sets split feasibility problem with splitting self-adaptive step size. This step size is calculated directly from the iteration process without need...

Authors: Yuchao Tang, Chuanxi Zhu and Hui Yu

Mann iteration process for monotone nonexpansive mappings

Authors: Buthinah Abdullatif Bin Dehaish and Mohamed Amine Khamsi

Some fixed point theorems in Menger probabilistic metric-like spaces

In this manuscript we extend very recent fixed point theorems in the setting of Menger spaces in three senses: on the one hand, we introduce the notion of Menger probabilistic metric-like space by avoiding a non-...

Authors: Antonio Francisco Roldán López de Hierro and Manuel de la Sen

Nielsen type numbers and homotopy minimal periods for maps on solvmanifolds with \(\operatorname{Sol}_{1}^{4}\)-geometry

Authors: Jang Hyun Jo and Jong Bum Lee

Common fixed point theorems for Geraghty’s type contraction mappings using the monotone property with two metrics

The main aim of this paper is to obtain some new common fixed point theorems for Geraghty’s type contraction mappings using the monotone property with two metrics and to give some examples to illustrate the ma...

Authors: Juan Martínez-Moreno, Wutiphol Sintunavarat and Yeol Je Cho

Some results in fixed point theory and application to the convergence of some iterative processes

In this paper, we study the existence and uniqueness of fixed points for a class of self-mappings satisfying certain rational expressions on closed, bounded and convex subsets with normal structures in reflexi...

Authors: Najeh Redjel and Abdelkader Dehici

Stability and convergence of a new composite implicit iterative sequence in Banach spaces

The purpose of this paper is to study stability and strong convergence of asymptotically pseudocontractive mappings by using a new composite implicit iteration process in an arbitrary real Banach space. The re...

Authors: Liping Yang and Weiming Kong

Coincidence point and fixed point theorems for a new type of G-contraction multivalued mappings on a metric space endowed with a graph

In this paper, a new type of G-contraction multivalued mappings in a metric space endowed with a directed graph is introduced and studied. This type of mappings is more general than that of Mizoguchi and Takahash...

Authors: Adisak Hanjing and Suthep Suantai

A discussion on best proximity point and coupled best proximity point in partially ordered metric spaces

In this paper we establish some best proximity point results using generalized weak contractions with discontinuous control functions. The theorems are established in metric spaces with a partial order. We vie...

Authors: Binayak S Choudhury, Nikhilesh Metiya, Mihai Postolache and Pulak Konar

Scalar gap functions and error bounds for generalized mixed vector equilibrium problems with applications

It is well known that equilibrium problems are very important mathematical models and are closely related with fixed point problems, variational inequalities, and Nash equilibrium problems. Gap functions and e...

Authors: Wenyan Zhang, Jiawei Chen, Shu Xu and Wen Dong

Modified semi-implicit midpoint rule for nonexpansive mappings

The purpose of the paper is to construct iterative methods for finding the fixed points of nonexpansive mappings. We present a modified semi-implicit midpoint rule with the viscosity technique. We prove that t...

Authors: Yonghong Yao, Naseer Shahzad and Yeong-Cheng Liou

Common fixed point results for four maps satisfying ϕ-contractive condition in multiplicative metric spaces

In this paper, we consider the setting of multiplicative metric spaces to establish results regarding the common fixed points of four mappings, using a contraction condition defined by means of a comparison fu...

Authors: Feng Gu and Yeol Je Cho

Common fixed point theorems for generalized cyclic contraction pairs in b-metric spaces with applications

In this paper, we introduce the notion of generalized cyclic contraction pairs in b-metric spaces and establish some fixed point theorems for such pairs. Also, we give some examples to illustrate the main results...

Authors: Oratai Yamaod, Wutiphol Sintunavarat and Yeol Je Cho