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  1. Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward ste...

    Authors: Minh N. Dao and Hung M. Phan

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:16

    Content type: Research

    Published on:

  2. It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the pot...

    Authors: Regina S. Burachik, Bethany I. Caldwell and C. Yalçın Kaya

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:15

    Content type: Research

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  3. In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation an...

    Authors: Malek Abbasi and Michel Théra

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:14

    Content type: Research

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  4. We explore a new approach for training neural networks where all loss functions are replaced by hard constraints. The same approach is very successful in phase retrieval, where signals are reconstructed from m...

    Authors: Veit Elser

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:12

    Content type: Research

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  5. Nonlinear fractional differential equations have been intensely studied using fixed point theorems on various different function spaces. Here we combine fixed point theory with complex analysis, considering sp...

    Authors: Arran Fernandez, Sümeyra Uçar and Necati Özdemir

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:11

    Content type: Research

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  6. This paper proposes a stochastic approximation method for solving a convex stochastic optimization problem over the fixed point set of a quasinonexpansive mapping. The proposed method is based on the existing ...

    Authors: Hideaki Iiduka

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:10

    Content type: Research

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  7. String-averaging is an algorithmic structure used when handling a family of operators in situations where the algorithm in hand requires to employ the operators in a specific order. Sequential orderings are we...

    Authors: Yair Censor and Ariel Nisenbaum

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:9

    Content type: Research

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  8. This paper studies uniqueness of solutions for a nonlinear Hadamard-type integro-differential equation in the Banach space of absolutely continuous functions based on Babenko’s approach and Banach’s contractio...

    Authors: Chenkuan Li

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:7

    Content type: Research

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  9. In this paper, we introduce and study a modified multi-step Noor iterative procedure with errors for two Lipschitz strictly hemicontractive-type mappings in arbitrary Banach spaces and constitute its convergen...

    Authors: Md. Asaduzzaman

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:6

    Content type: Research

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  10. We propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudom...

    Authors: Konrawut Khammahawong, Poom Kumam, Parin Chaipunya and Somyot Plubtieng

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:5

    Content type: Research

    Published on:

  11. In this paper, we investigate the existence and the uniqueness of a common fixed point of a pair of self-mappings satisfying new contractive type conditions on a modular metric space endowed with a reflexive d...

    Authors: Karim Chaira, Abderrahim Eladraoui, Mustapha Kabil and Abdessamad Kamouss

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:4

    Content type: Research

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  12. In the literature there are several methods for comparing two convergent iterative processes for the same problem. In this note we have in view mostly the one introduced by Berinde in (Fixed Point Theory Appl....

    Authors: Constantin Zălinescu

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:2

    Content type: Research

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  13. In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and differe...

    Authors: Zhiqun Xue and Guiwen Lv

    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:1

    Content type: Research

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  14. In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imp...

    Authors: Yuanheng Wang, Xiuping Wu and Chanjuan Pan

    Citation: Fixed Point Theory and Applications 2020 2020:18

    Content type: Research

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  15. In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in un...

    Authors: Noureddine El Harmouchi, Karim Chaira and El Miloudi Marhrani

    Citation: Fixed Point Theory and Applications 2020 2020:17

    Content type: Research

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  16. In this paper, fixed point results for a newly introduced Geraghty quasi-contraction type mappings are proved in more general metric spaces called T-orbitally complete dislocated quasi-metric spaces. Geraghty qua...

    Authors: Joy C. Umudu, Johnson O. Olaleru and Adesanmi A. Mogbademu

    Citation: Fixed Point Theory and Applications 2020 2020:16

    Content type: Research

    Published on:

  17. An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studie...

    Authors: Charles E. Chidume, Poom Kumam and Abubakar Adamu

    Citation: Fixed Point Theory and Applications 2020 2020:12

    Content type: Research

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  18. In this paper, we provide common fixed point theorems for two and three commuting mappings which generalize Darbo’s fixed point theorem. An explicit example is given for illustration.

    Authors: Meryeme El Harrak and Ahmed Hajji

    Citation: Fixed Point Theory and Applications 2020 2020:11

    Content type: Research

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  19. In this paper, we introduce a self-adaptive inertial subgradient extragradient method for solving pseudomonotone equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm consist...

    Authors: Lateef Olakunle Jolaoso and Maggie Aphane

    Citation: Fixed Point Theory and Applications 2020 2020:9

    Content type: Research

    Published on:

  20. In this paper, we use Suzuki-type contraction to prove three fixed point theorems for generalized contractions in an ordered space equipped with two metrics; we obtain some generalizations of the Kannan fixed ...

    Authors: Outass Rida, Chaira Karim and Marhrani El Miloudi

    Citation: Fixed Point Theory and Applications 2020 2020:7

    Content type: Research

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  21. Set-valued contractions of Leader type in quasi-triangular spaces are constructed, conditions guaranteeing the existence of nonempty sets of periodic points, fixed points and endpoints of such contractions are...

    Authors: Kazimierz Włodarczyk

    Citation: Fixed Point Theory and Applications 2020 2020:6

    Content type: Research

    Published on:

  22. The Editors-in-Chief have retracted this article [1] because it showed evidence of peer review manipulation. In addition, the identity of the corresponding author could not be verified: Nagoya University have ...

    Authors: Zhenhai Yan, Guojun Yan and Ikudol Miyamoto

    Citation: Fixed Point Theory and Applications 2020 2020:5

    Content type: Retraction Note

    Published on:

    The original article was published in Fixed Point Theory and Applications 2015 2015:197

  23. The Editors-in-Chief have retracted this article [1] because it overlaps significantly with a number of previously published articles from different authors [2-4] and one article by different authors that was ...

    Authors: Zhiqiang Li and Beatriz Ychussie

    Citation: Fixed Point Theory and Applications 2020 2020:2

    Content type: Retraction Note

    Published on:

    The original article was published in Fixed Point Theory and Applications 2015 2015:89

  24. The Editors-in-Chief have retracted this article [1] because the results presented are invalid. The article also shows significant overlap with a number of previously published articles [2–5] and evidence of b...

    Authors: Gaixian Xue and Eve Yuzbasi

    Citation: Fixed Point Theory and Applications 2020 2020:1

    Content type: Retraction Note

    Published on:

    The original article was published in Fixed Point Theory and Applications 2015 2015:34

  25. The purpose of this paper is to define a new random operator called the generalized ϕ-weakly contraction of the rational type. This new random operator includes those studied by Khan et al. (Filomat 31(12):3611–3...

    Authors: Godwin Amechi Okeke, Sheila Amina Bishop and Hudson Akewe

    Citation: Fixed Point Theory and Applications 2019 2019:15

    Content type: Research

    Published on:

  26. In this paper, we define F-contractive type mappings in b-metric spaces and prove some fixed point results with suitable examples. F-expanding type mappings are also defined and a fixed point result is obtained.

    Authors: Nilakshi Goswami, Nehjamang Haokip and Vishnu Narayan Mishra

    Citation: Fixed Point Theory and Applications 2019 2019:13

    Content type: Research

    Published on:

  27. In this paper, we introduce and discuss soft single points, which proceed towards soft real points by using real numbers and subsets of set of real numbers. We also define the basic operations on soft real poi...

    Authors: Sabir Hussain, Hurmet Fulya Akiz and Amlak Ibrahim Alajlan

    Citation: Fixed Point Theory and Applications 2019 2019:9

    Content type: Research

    Published on:

  28. The primary objective of this paper is the study of the generalization of some results given by Basha (Numer. Funct. Anal. Optim. 31:569–576, 2010). We present a new theorem on the existence and uniqueness of bes...

    Authors: Mohamed Iadh Ayari, Zead Mustafa and Mohammed Mahmoud Jaradat

    Citation: Fixed Point Theory and Applications 2019 2019:7

    Content type: Research

    Published on:

  29. In this paper, we establish a new iteration method, called an InerSP (an inertial S-iteration process), by combining a modified S-iteration process with the inertial extrapolation. This strategy is for speedin...

    Authors: Aniruth Phon-on, Nifatamah Makaje, Areeyuth Sama-Ae and Kittiya Khongraphan

    Citation: Fixed Point Theory and Applications 2019 2019:4

    Content type: Research

    Published on:

  30. In this article, we carry out some observations on existing metrical coincidence theorems of Karapinar et al. (Fixed Point Theory Appl. 2014:92, 2014) and Erhan et al. (J. Inequal. Appl. 2015:52, 2015) proved for...

    Authors: Aftab Alam, Mohammad Imdad and Mohammad Arif

    Citation: Fixed Point Theory and Applications 2019 2019:6

    Content type: Research

    Published on:

  31. We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoi...

    Authors: Marek Izydorek, Joanna Janczewska and Nils Waterstraat

    Citation: Fixed Point Theory and Applications 2019 2019:5

    Content type: Research

    Published on:

  32. In this paper, we study the class of further generalized hybrid mappings due to Khan (Fixed Point Theory Appl. 2018:8, 2018) in the setting of Hadamard spaces. We prove a demiclosed principle for such mappings in...

    Authors: Asawathep Cuntavepanit and Withun Phuengrattana

    Citation: Fixed Point Theory and Applications 2019 2019:3

    Content type: Research

    Published on:

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