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

Turab, Ali; Bakery, Awad A.; Mohamed, OM Kalthum S. K.; Ali, Wajahat

doi:10.1155/2022/1064803

Cited by 3 publications

(1 citation statement)

References 24 publications

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“…The above functional equation (1.4) is used to describe the relationship between predator animals and their two prey choices. Numerous research on human and animals behavior in such situations have generated notable findings (for the detail, see [5,9,14,15,28,29,30,21]). On the other hand, the theory of fixed points is concerned with the conditions that ensure the existence of points x in a set Y that satisfies an operator equation x = Gx, where G is a transformation defined on a set Y .…”

Section: Operators For Reinforcement-extinction Modelmentioning

confidence: 99%

On the solution of the generalized functional equation arising in mathematical psychology and theory of learning approached by the Banach fixed point theorem

TURAB¹,

SINTUNAVARAT²

2022

CJM

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In mathematical psychology, the model of decision practice represents the development of moral judgment that deals with the time to decide the meaning of the various choices and selecting one of them for use. Most animal behavior research classifies such situations as two distinct phenomena. On the other hand, reward plays a big part in this kind of study since, based on the selected side and food location, such circumstances may be classified into four categories. This paper intends to investigate such types of behavior and establish a general functional equation for it. The proposed functional equation can be used to describe several psychological and learning theory models in the existing literature. By using the fixed point theory tools, we obtain the results related to the existence, uniqueness, and stability of a solution to the proposed functional equation. Finally, we give two examples to support our main results.

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Section: Operators For Reinforcement-extinction Modelmentioning

confidence: 99%

On the solution of the generalized functional equation arising in mathematical psychology and theory of learning approached by the Banach fixed point theorem

TURAB¹,

SINTUNAVARAT²

2022

CJM

View full text Add to dashboard Cite

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On a unique solution and stability analysis of a class of stochastic functional equations arising in learning theory

Turab

2022

Analysis

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Numerous computational and learning theory models have been studied using probabilistic functional equations. Especially in two-choice scenarios, the vast bulk of animal behavior research divides such situations into two different events. They split these actions into two possibilities according to the animals’ progress toward a particular decision. However, reward plays a crucial role in such experiments because, based on the selected side and the food placement, such scenarios may be classified into four distinct categories. This article aims to explore the animals’ reactions to such circumstances by presenting a generic stochastic functional equation. By using the well-known fixed point theory results, we examine the existence, uniqueness, and stability of solutions to the suggested functional equation. Moreover, an example is included to emphasize the significance of our findings.

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The existence and uniqueness of solutions to a functional equation arising in psychological learning theory

Turab

Rosli

Ali

et al. 2023

Demonstratio Mathematica

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The paradigm of choice practice represents the psychological theory of learning in the development of moral judgment. It is concerned with evaluating the implications of several choices and selecting one of them to implement. The goal of this work is to provide a generic functional equation to observe the behavior of animals in such circumstances. Our suggested functional equation can be employed to describe several well-known psychology and learning theories. The fixed point theorem proposed by Banach is utilized to show that the solution of a given functional problem exists and is unique. In addition, the stability of the given functional equation’s solution is discussed in terms of the Hyers-Ulam and Hyers-Ulam-Rassias results. Furthermore, two examples are provided to highlight the relevance of the significant outcomes in the context of the literature.

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

Cited by 3 publications

References 24 publications

On the solution of the generalized functional equation arising in mathematical psychology and theory of learning approached by the Banach fixed point theorem

On the solution of the generalized functional equation arising in mathematical psychology and theory of learning approached by the Banach fixed point theorem

On a unique solution and stability analysis of a class of stochastic functional equations arising in learning theory

The existence and uniqueness of solutions to a functional equation arising in psychological learning theory

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