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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. Research

    Common best proximity points results for new proximal C-contraction mappings

    We define a new version of proximal C-contraction and prove the existence and uniqueness of a common best proximity point for a pair of non-self functions. Then we apply our main results to get some fixed point t...

    Parvaneh Lo’lo’, Seiyed Mansour Vaezpour and Reza Saadati

    Fixed Point Theory and Applications 2016 2016:56

    Published on: 30 April 2016

  2. Research

    Coupled fixed point theorems for single-valued operators in b-metric spaces

    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 ...

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

    Fixed Point Theory and Applications 2015 2015:231

    Published on: 22 December 2015

  3. Research

    A fixed point result and the stability problem in Lie superalgebras

    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 ...

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

    Fixed Point Theory and Applications 2015 2015:219

    Published on: 26 November 2015

  4. Research

    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...

    Zhangsong Yao, Shin Min Kang and Hong-Jun Li

    Fixed Point Theory and Applications 2015 2015:206

    Published on: 14 November 2015

  5. Research

    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...

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

    Fixed Point Theory and Applications 2015 2015:207

    Published on: 14 November 2015

  6. Research

    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, ...

    Huichun Hua, Minjiang Chen and Shenghua Wang

    Fixed Point Theory and Applications 2015 2015:201

    Published on: 6 November 2015

  7. Research

    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...

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

    Fixed Point Theory and Applications 2015 2015:179

    Published on: 6 October 2015

  8. Research

    Endpoints of multivalued nonexpansive mappings in geodesic spaces

    Let X be either a uniformly convex Banach space or a reflexive Banach space having the Opial property. It is shown that a multivalued nonexpansive mapping on a bounded closed convex subset of X has an endpoint if...

    Bancha Panyanak

    Fixed Point Theory and Applications 2015 2015:147

    Published on: 19 August 2015

  9. Research

    Mathematical programming for the sum of two convex functions with applications to lasso problem, split feasibility problems, and image deblurring problem

    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...

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

    Fixed Point Theory and Applications 2015 2015:143

    Published on: 19 August 2015