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  1. The main goal of this paper is to study a class of differential nonlinear system involving parabolic variational and history-dependent hemivariational inequalities in Banach spaces by using the penalty method....

    Authors: Xu Chu, Tao Chen, Nan-jing Huang and Yi-bin Xiao
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:17
  2. This work establishes the existence of a weak solution to a new model for the process of debonding of two elastic 2D-bars caused by humidity and vibrations. A version of the model was first presented in the PC...

    Authors: Meir Shillor and Kenneth L. Kuttler
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:15
  3. We consider a nonlinear elasticity problem in a bounded domain, its boundary is decomposed in three parts: lower, upper, and lateral. The displacement of the substance, which is the unknown of the problem, is ...

    Authors: Mahdi Boukrouche, Boubakeur Merouani and Fayrouz Zoubai
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:14
  4. In this paper, we introduce the class of rectangular quasi b-metric spaces as a generalization of rectangular metric spaces, rectangular quasi-metric spaces, rectangular b-metric spaces, define generalized

    Authors: Bontu Nasir Abagaro, Kidane Koyas Tola and Mustefa Abduletif Mamud
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:13
  5. As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for non-matching meshes. In (Wriggers et al. in Comput. Mech. 58...

    Authors: Fei Wang and B. Daya Reddy
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:10
  6. In this paper, an inertial S-iteration iterative process for approximating a common fixed point of a finite family of quasi-Bregman nonexpansive mappings is introduced and studied in a reflexive Banach space. ...

    Authors: Bashir Ali and Aisha A. Adam
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:9
  7. In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are ...

    Authors: Jamal Eddine Lazreg, Nadia Benkhettou, Mouffak Benchohra and Erdal Karapinar
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:6
  8. In this paper we give a simple proof of three fixed point theorems of Secelean and Wardowski by using the fixed point result of Jachymski et al. Our result is established with weaker assumptions than the three...

    Authors: Satit Saejung and Pinya Ardsalee
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:7
  9. We consider an abstract inclusion in a real Hilbert space, governed by an almost history-dependent operator and a time-dependent multimapping with prox-regular values. We establish the unique solvability of th...

    Authors: Florent Nacry and Mircea Sofonea
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:5
  10. We study a mechanical system with a finite number of degrees of freedom, subjected to perfect time-dependent frictionless unilateral (possibly nonconvex) constraints with inelastic collisions on active constra...

    Authors: Samir Adly and Nguyen Nang Thieu
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:3
  11. This paper starts off by the celebrated Knaster–Kuratowski–Mazurkiewicz principle in the formulation by Ky Fan. We provide a novel variant of this principle and build an existence theory for extended real-valu...

    Authors: Joachim Gwinner
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:4
  12. The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Sinc...

    Authors: G. H. M. Araújo, R. Arefidamghani, R. Behling, Y. Bello-Cruz, A. Iusem and L.-R. Santos
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:1
  13. Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of...

    Authors: Pontus Giselsson and Walaa M. Moursi
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:25
  14. This paper is devoted to numerical analysis of doubly-history dependent variational inequalities in contact mechanics. A fully discrete method is introduced for the variational inequalities, in which the doubl...

    Authors: Wei Xu, Cheng Wang, Mingyan He, Wenbin Chen, Weimin Han and Ziping Huang
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:24
  15. In 1990, Romero presented a beautiful formula for the projection onto the set of rectangular matrices with prescribed row and column sums. Variants of Romero’s formula were rediscovered by Khoury and by Glunt,...

    Authors: Heinz H. Bauschke, Shambhavi Singh and Xianfu Wang
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:23
  16. Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to e...

    Authors: Howard Heaton, Samy Wu Fung, Aviv Gibali and Wotao Yin
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:21
  17. By the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generali...

    Authors: Sjur Didrik Flåm
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:20
  18. We study the Stokes problem for the incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral boundary condition, the Navier slip condition, a nonmo...

    Authors: Jing Zhao, Stanisław Migórski and Sylwia Dudek
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:19
  19. In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest...

    Authors: Pattanapong Tianchai
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:18
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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

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