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AIMS Mathematics

2022, Volume 7, Issue 4: 5291-5304. doi: 10.3934/math.2022294
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Research article

A unified fixed point approach to study the existence and uniqueness of solutions to the generalized stochastic functional equation emerging in the psychological theory of learning

  • 1.
    Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12120, Thailand
  • 2.
    School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
  • 3.
    Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
  • Received: 09 August 2021 Revised: 26 December 2021 Accepted: 03 January 2022 Published: 05 January 2022

  • MSC : 39B22, 47H10, 03C45

  • The model of decision practice reflects the evolution of moral judgment in mathematical psychology, which is concerned with determining the significance of different options and choosing one of them to utilize. Most studies on animals behavior, especially in a two-choice situation, divide such circumstances into two events. Their approach to dividing these behaviors into two events is mainly based on the movement of the animals towards a specific choice. However, such situations can generally be divided into four events depending on the chosen side and placement of the food. This article aims to fill such gaps by proposing a generic stochastic functional equation that can be used to describe several psychological and learning theory experiments. The existence, uniqueness, and stability analysis of the suggested stochastic equation are examined by utilizing the notable fixed point theory tools. Finally, we offer two examples to substantiate our key findings.

    Citation: Ali Turab, Wajahat Ali, Choonkil Park. A unified fixed point approach to study the existence and uniqueness of solutions to the generalized stochastic functional equation emerging in the psychological theory of learning[J]. AIMS Mathematics, 2022, 7(4): 5291-5304. doi: 10.3934/math.2022294

    Related Papers:

  • The model of decision practice reflects the evolution of moral judgment in mathematical psychology, which is concerned with determining the significance of different options and choosing one of them to utilize. Most studies on animals behavior, especially in a two-choice situation, divide such circumstances into two events. Their approach to dividing these behaviors into two events is mainly based on the movement of the animals towards a specific choice. However, such situations can generally be divided into four events depending on the chosen side and placement of the food. This article aims to fill such gaps by proposing a generic stochastic functional equation that can be used to describe several psychological and learning theory experiments. The existence, uniqueness, and stability analysis of the suggested stochastic equation are examined by utilizing the notable fixed point theory tools. Finally, we offer two examples to substantiate our key findings.


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