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New Challenges and Trends in Fixed Point Theory and Its Applications

This thematic series is devoted to publishing the latest and most significant research on Fixed Point Theory including its wide range of applications. Its goals are to stimulate further research and to highlight and emphasize the most recent advances in the field as well as to promote, encourage, and bring together researchers in Fixed point Theory and Applications including those interested in potential applications in Science and Engineering.

Edited by: Yeol Je Cho, Manuel De la Sen, Abdul Latif and Reza Saadati

  1. Content type: Research

    This paper provides new common fixed point theorems for pairs of multivalued and single-valued mappings operating between ordered Banach spaces. Our results lead to new existence theorems for a system of integ...

    Authors: Nawab Hussain and Mohamed-Aziz Taoudi

    Citation: Fixed Point Theory and Applications 2016 2016:65

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  2. Content type: Research

    In this paper we consider a class of bilevel variational inequalities with hierarchical nesting structure. We first of all get the existence of a solution for this problem by using the Himmelberg fixed point t...

    Authors: Gaoxi Li, Zhongping Wan, Jia-wei Chen and Xiaoke Zhao

    Citation: Fixed Point Theory and Applications 2016 2016:41

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  3. Content type: Research

    Motivated by Gopal et al. (Acta Math. Sci. 36B(3):1-14, 2016). We introduce the notion of α-type F-contraction in the setting of modular metric spaces which is independent from one given in (Hussain et al. in Fix...

    Authors: Anantachai Padcharoen, Dhananjay Gopal, Parin Chaipunya and Poom Kumam

    Citation: Fixed Point Theory and Applications 2016 2016:39

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  4. Content type: Research

    In this paper, we establish the existence of a common fixed point of almost generalized contractions on modular spaces. As an application, we present some fixed and common fixed point results for such mappings...

    Authors: Mahpeyker Öztürk, Mujahid Abbas and Ekber Girgin

    Citation: Fixed Point Theory and Applications 2016 2016:19

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  5. Content type: Research

    In this paper, we propose an iterative algorithm and, by using the proposed algorithm, prove some strong convergence theorems for finding a common element of the set of solutions of a finite family of split eq...

    Authors: Shenghua Wang, Xiaoying Gong, Afrah AN Abdou and Yeol Je Cho

    Citation: Fixed Point Theory and Applications 2016 2016:4

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  6. Content type: Research

    In this paper, we introduce the two new concepts of an α-type almost-F-contraction and an α-type F Suzuki contraction and prove some fixed point theorems for such mappings in a complete metric space. Some example...

    Authors: Lokesh Budhia Budhia, Poom Kumam, Juan Martínez-Moreno and Dhananjay Gopal

    Citation: Fixed Point Theory and Applications 2016 2016:2

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  7. Content type: Research

    We compare the rate of convergence for some iteration methods for contractions. We conclude that the coefficients involved in these methods have an important role to play in determining the speed of the conver...

    Authors: Shahin Fathollahi, Adrian Ghiura, Mihai Postolache and Shahram Rezapour

    Citation: Fixed Point Theory and Applications 2015 2015:234

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  8. Content type: Research

    The aim of this paper to present fixed point results for single-valued operators in b-metric spaces. The case of scalar metric and the case of vector-valued metric approaches are considered. As an application, a ...

    Authors: Monica-Felicia Bota, Adrian Petruşel, Gabriela Petruşel and Bessem Samet

    Citation: Fixed Point Theory and Applications 2015 2015:231

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  9. Content type: Research

    In this paper, we introduce the concept of normed Lie superalgebras and define the superhomomorphism and the superderivation in normed Lie superalgebras. We define a generalized T-orbitally complete metric space ...

    Authors: Madjid Eshaghi, Sadegh Abbaszadeh, Manuel de la Sen and Zahra Farhad

    Citation: Fixed Point Theory and Applications 2015 2015:219

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  10. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:212

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  11. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:205

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  12. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:207

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  13. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:179

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  14. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:174

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  15. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:171

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  16. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:169

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  17. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:170

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  18. Content type: Research

    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

    Citation: Fixed Point Theory and Applications 2015 2015:164

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  19. Content type: Research

    In this paper, two iteration processes are used to find the solutions of the mathematical programming for the sum of two convex functions. In infinite Hilbert space, we establish two strong convergence theorem...

    Authors: Chih Sheng Chuang, Zenn-Tsun Yu and Lai-Jiu Lin

    Citation: Fixed Point Theory and Applications 2015 2015:143

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