Fixed points of multivalued non-linear F-contractions with application to solution of matrix equations

The term “learning” is often used to refer to a generally stable behavioral change resulting from practice. However, it is a fundamental biological capacity far more developed in humans than in other living beings. In an animal or human being, the learning phase may often be viewed as a series of choices between multiple possible reactions. Here, we analyze a specific type of human learning process related to gambling in which a subject inserts a poker chip to operate a two-armed bandit device and then presses one of the two keys. Through the use of an electromagnet, one or more poker chips are given to the individual in a container located in the apparatus’s center. If a chip is provided, it is declared a winner; otherwise, it is considered a loser. The goal of this paper is to look at the subject’s actions in such situations and provide a mathematical model that is appropriate for it. The existence of a unique solution to the suggested human learning model is examined using relevant fixed point results.

Section: Mathematical Modeling Of the Two-armed Bandit Experimentsmentioning

confidence: 99%

On a Unique Solution of the Stochastic Functional Equation Arising in Gambling Theory and Human Learning Process

Turab

Bakery

Mohamed

et al. 2022

“…It has been generalized and extended in various directions (for the detail, see [13][14][15][16]). For more details about the fixed point theory and its applications in different spaces, we refer the reader to [17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

On a Unique Solution of a T-Maze Model Arising in the Psychology and Theory of Learning

Turab

Ali

Nieto

2022

In the form of a T, a T-maze is an experimental design in which each trial consists of decisions between two or more options. It contains choices with particular kinds of symmetries that have gained considerable attention in psychology and learning theories. One of the simplest mazes utilized by rats is the T-maze since it requires just a single point of preference. At a T-maze base, the mouse chooses to turn right or left to get food. This paper aims at analyzing the rat’s behavior in such circumstances and proposing a suitable mathematical model for it. The existence and uniqueness of a solution to the proposed T-maze model are investigated by using the appropriate fixed point method.

“…After this, many authors generalized the F-contraction in several ways (see [12][13][14][15][16][17][18][19][20][21][22] and references therein). In 2015, Klim and Wardowski [23] extended the concept of F -contractive mappings to the case of nonlinear F-contractions and proved fixed point theorems via the dynamic processes.…”

Section: Introductionmentioning

confidence: 99%

Fixed Point, Data Dependence, and Well-Posed Problems for Multivalued Nonlinear Contractions

Iqbal

Hussain

Alsulami

et al. 2021

Self Cite

The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. Furthermore, the existence and data dependence findings for these multivalued operators are obtained. A nontrivial example is also provided to support the results. The results generalize, improve, and extend existing results in the literature.