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Workshop on Iterative Approximation of Fixed Points

11:10 | A modified iterative approaches for solving fixed-point and minimization problems in Positive curvature metric spaces ABSTRACT. In this paper, we propose a new modified proximal point algorithm in the setting of CAT(1) spaces which can be used for solving minimization problems and common fixed point problem. Also, we prove few convergence results of the proposed algorithm under some mild conditions. In process, several relevant results of the existing literature are generalized and improved. |

11:30 | An iterative method with inertial extrapolation effect for solving multiple-sets split feasibility problem PRESENTER: Guash Haile Taddele ABSTRACT. An iterative method with inertial extrapolation term for approximating the solution of multiple-sets split feasibility problem in the infinite-dimensional Hilbert spaces is presented. In a recent paper (Advances in Pure and Applied Mathematics, vol.10, no.4, pp. 339-353, 2019), Ogbuisi and Mewomo introduced an iterative algorithm involving an inertial term and a step size independent of the operator norm for approximating a solution to split variational inequality problem in a real Hilbert space. We extend the algorithm introduced by Ogbuisi and Mewomo for solving multiple-set split feasibility problem, and we propose a self-adaptive technique to choose the stepsizes such that the implementation of our algorithm does not need prior information about the operator norm. We prove a weak convergence theorem to the proposed algorithm under some suitable conditions. Finally, we give some numerical examples to illustrate the efficiency and implementation of our method compared to some existing results. |

11:50 | A Viscosity-type Scheme for Optimization Problems in Hadamard Spaces With Applications ABSTRACT. This article proposes a viscosity-type scheme for approximating a common solution of convex minimization problem, monotone vector field inclusion problem and fixed point problem involving multivalued nonexpansive mapping in the framework of Hadamard spaces. We establish a strong convergence theorem for the sequence generated therefrom to a solution of the problem. Furthermore, we apply our results to compute the Fr{\'e}chet mean, find the mean of probabilities, minimize the energy of measurable mappings and solve a problem of two-arm robotic motion control. Finally, we give a numerical example to demonstrate the applicability of the method and also issue comparisons with some existing methods. Our results extend and complement some recent results in the literature. |

12:10 | An Inertial Iterative Method for Solving the Split Variational Inclusion Problems in Hilbert Space ABSTRACT. In this paper, we introduced a new inertial iterative method by combining inertial method together with proximal point algorithm for solving split variational inclusion problems in real Hilbert spaces. Under some suitable conditions, we have shown the strong convergence theorem for the sequence generated by the proposed iterative method. Furthermore, we applied our proposed algorithm to derive iterative methods for solving split feasibility problem and split minimization problem. Additionally, we present some numerical experiments to illustrate the convergence behaviour of the proposed method in comparisons with some existing methods in the literature and possible application of the proposed method in recovering a an original signal from a sparse and noisy signal. |

12:30 | Modified Halpern Type Algorithms of Common Solutions to Fixed Points Problems and Inclusion Problems on Hadamard Manifolds PRESENTER: Konrawut Khammahawong ABSTRACT. This paper deals with the modified Halpern type iterative algorithm for finding a common solution from the sets of fixed points and singularities of an inclusion problem which is defined by the sum of strongly monotone vector field and multivalued maximal monotone vector field on Hadamard manifolds. Under appropriate assumptions, we prove convergence theorems for approximating the common solutions of the proposed problem in Hadamard manifolds. |

Workshop on Iterative Approximation of Fixed Points

14:00 | Some New Results for Fixed Point Theory in Modular Spaces ABSTRACT. This study purposes achieving some consequences related to fixed and common fixed point theory using various concepts in modular spaces. |

14:20 | On Common Fixed Point Theorems Satisfying Z_Σ-⊥-Contraction Mappings in Orthogonal Modular b-Metric Spaces ABSTRACT. In this paper, by considering the notion of orthogonal sets and modular b−metric function we introduce orthogonal modular b−metric spaces. Moreover, we establish some common fixed point theorems for Σ−type contractions involving generalized simulative-Proinov function and in the setting of orthogonal modular b−metric spaces. |

14:40 | Common fixed points of generalized (alpha,beta )-Geraghty-Simulative contraction in non-Archimedean modular metric spaces PRESENTER: Mahpeyker Öztürk ABSTRACT. In this paper, by using the concept of cyclic $(\alpha,\beta)$-admissible pair, Geraghty contractions and simulation functions, we establish the existence and uniqueness of common fixed point of a generalized $(\alpha,\beta)-$Geraghty simulative contraction on non-Archimedean modular metric spaces. Our results generalize and extend various comparable results in the existing literature. As an application, we acquire common fixed point results in non-Archimedean modular metric spaces with a directed graph. |

15:00 | On graphic p-convex contractions ABSTRACT. The aim of this work is to prove new results regarding the Picard iteration of a graphic p-convex contraction in the metric space framework. |

Workshop on Iterative Approximation of Fixed Points

Working Formal Methods Symposium

17:10 | How the Events in the Life of Painters Influence the Colors of their Paintings PRESENTER: Ada-Astrid Mocanu ABSTRACT. Out of the desire to observe the interdisciplinary usefulness of Computer Science, we decided to begin a study about the surrounding world. Starting from the visual world, we outlined a basic question: Do events we experience in our lives influence our artistic capabilities? We begin by collecting all the necessary data about several painters and then extracting the predominant colors of their paintings. Using Machine Learning techniques, we compared the efficiency of different algorithms, measuring the efficiency score in the CIELAB Color Space. Then, based on Natural Language Processing elements and painters’ biographical information, we built a timeline of the events from the painter’s lives, enriched with the predominant colors used by them. Wanting to observe the human perspective about the feelings derived from the paintings, we build a small form-like application to extract this information from volunteers in the field. Correlating the algorithms’ results with those extracted from human subjects, we showed that periods of happiness and unhappiness bounded with the colors used by painters. These results lead us to the conclusion that this topic deserves further study in order to obtain more accurate information and to be able to move on to its use in practical applications. |

17:30 | Creating a Dataset and Models Based on Convolutional Neural Networks to Improve Fruit Classification PRESENTER: Mihai-Dimitrie Minut ABSTRACT. We are often curious to find out what fruit is found in a tree when we are walking through parks or a botanical garden. Fruit classification is a complex activity that depends on the datasets used and the deep learning methods applied to them. This paper aims to present the steps by which we created a dataset with 262 fruits, and then how we created several models based on it. Evaluation and testing have shown us that the resource and models created can be useful to those who want to create applications that recognize fruits. |

17:50 | Glacier Movement Prediction through Computer Vision and Satellite Imagery PRESENTER: Maria-Minerva Vonica ABSTRACT. Over the last decade, climate change has impacted Earths' atmosphere and environment more than anytime before. Glaciers are the most sensitive indicators of its impact. In this work, we model a glacier's evolution by applying computer vision algorithms on high-resolution satellite imagery. We detect changes in the ice coverage movement by applying a dense optical flow algorithm over an image time series covering a particular scene (region) and processed to extract the NDSI. We perform tests on the Jungfrau-Aletsch-Bietschhorn (JAB) glacier in the Swiss Alps. Our results show that we are able to obtain relevant information by computing motion vectors across time. Furthermore, we observe small differences between our predicted NDSI and the observed values demonstrating the efficiency of the approach. In addition, by applying various machine learning techniques we provide an optimistic date for when the JAB glacier will completely disappear: 2800. |

Workshop on Iterative Approximation of Fixed Points