Yazar "Gursoy, Faik" seçeneğine göre listele

Listeleniyor 1 - 5 / 5
  • Küçük Resim Yok
    Öğe
    An Efficient Inertial Type Iterative Algorithm to Approximate the Solutions of Quasi Variational Inequalities in Real Hilbert Spaces
    (Springer/Plenum Publishers, 2021) Keten Copur, Aysegul; Hacioglu, Emirhan; Gursoy, Faik; Erturk, Muzeyyen
    In this article, we design a projection type iterative algorithm with two inertial steps for solving quasi-variational inequalities with Lipschitz continuous and strongly monotone mappings in real Hilbert spaces. We establish different strong convergence results through this algorithm. We give a non-trivial example to validate one of our results and to illustrate the efficiency of the proposed algorithm compared with an already existing one. We also present some numerical experiments to demonstrate the potential applicability and computing performance of our algorithm compared with some other algorithms existing in the literature. The results obtained herein are generalizations and substantial improvements of some earlier results.
  • Küçük Resim Yok
    Öğe
    Iterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learning
    (Elsevier, 2021) Hacioglu, Emirhan; Gursoy, Faik; Maldar, Samet; Atalan, Yunus; Milovanovic, Gradimir V.
    In this paper, we revisit two recently published papers on the iterative approximation of fixed points by Kumam et al. (2019) [17] and Maniu (2020) [19] and reproduce convergence, stability, and data dependency results presented in these papers by removing some strong restrictions imposed on parametric control sequences. We confirm the validity and applicability of our results through various non-trivial numerical examples. We suggest a new method based on the iteration algorithm given by Thakur et al. (2014) [28] to solve the two-point second-order boundary value problems. Furthermore, based on the above mentioned iteration algorithm and S-iteration algorithm, we propose two new gradient type projection algorithms and applied them to supervised learning. In both applications, we present some numerical examples to demonstrate the superiority of the newly introduced methods in terms of convergence, accuracy, and computational time against some earlier methods. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
  • Küçük Resim Yok
    Öğe
    Monotone Generalized ?-Nonexpansive Mappings on CATp(0) Spaces
    (Springer, 2023) Hacioglu, Emirhan; Gursoy, Faik; Khan, Abdul Rahim
    We examine the existence of fixed points of generalized alpha-nonexpansive mappings on CAT(p)(0) spaces. We establish various convergence results for a newly defined algorithm associated with alpha-nonexpansive mappings and present some illustrative examples to show the efficiency of the proposed algorithm and to support the above-mentioned results. We also define monotone generalized alpha-nonexpansive mappings and prove some existence and convergence results for these mappings.
  • Küçük Resim Yok
    Öğe
    New insights on a pair of quasi-contractive operators in Banach spaces: Results on Jungck type iteration algorithms and proposed open problems
    (Elsevier, 2024) Copur, Aysegul Keten; Hacioglu, Emirhan; Gursoy, Faik
    In this paper, we explore relationships among the pairs of various well-known contractive type operators in Banach spaces. We also present a novel Jungck type iteration algorithm for a pair of quasi-contractive operators, which is thoroughly investigated in terms of strong convergence, stability, and data dependency. To demonstrate the efficacy of the proposed algorithm and reliability of each of the mentioned results, we furnish illustrative academic examples including both linear and nonlinear DEs. Furthermore, we present several open problems that warrant further study. Our results complement recent findings in the literature and contribute to further development in this area. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
  • Küçük Resim Yok
    Öğe
    Variational Inequality Problem Involving Multivalued Nonexpansive Mapping in CAT(0) Spaces
    (Springer Basel Ag, 2022) Gursoy, Faik; Hacioglu, Emirhan; Karakaya, Vatan; Milovanovic, Gradimir, V; Uddin, Izhar
    In this paper, we introduce a new type of variational inequality problem (VIP) involving nonself multivalued mappings in CAT(0) spaces. We show that this VIP problem admit a solution under suitable conditions. We also perform the convergence analysis of introduced VIP via proximal multivalued Picard-S iteration. We finish our paper with some convergence theorems for new iteration scheme and system of variational inequalities associated with finite family of nonself multivalued nonexpansive mappings.