scholarly journals 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

2022 ◽  
Vol 7 (4) ◽  
pp. 5291-5304
Author(s):  
Ali Turab ◽  
◽  
Wajahat Ali ◽  
Choonkil Park ◽  
◽  
...  
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Stochastic Equation ◽  
Fixed Point Theory ◽  
Psychological Theory ◽  
Point Theory ◽  
Mathematical Psychology ◽  
Choice Situation ◽  
Uniqueness Of Solutions ◽  
Stochastic Functional

<abstract><p>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.</p></abstract>

scholarly journals Terminal Value Problem for Differential Equations with Hilfer–Katugampola Fractional Derivative

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 672 ◽  
Author(s):  
Mouffak Benchohra ◽  
Soufyane Bouriah ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Terminal Value Problem

We present in this work the existence results and uniqueness of solutions for a class of boundary value problems of terminal type for fractional differential equations with the Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii’s fixed point theorem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes.

The stability of an additive functional equation in menger probabilistic φ-normed spaces

2011 ◽  
Vol 61 (5) ◽  
Author(s):  
D. Miheţ ◽  
R. Saadati ◽  
S. Vaezpour
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Stability Result ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
The Stability

AbstractWe establish a stability result concerning the functional equation: $\sum\limits_{i = 1}^m {f\left( {mx_i + \sum\limits_{j = 1,j \ne i}^m {x_j } } \right) + f\left( {\sum\limits_{i = 1}^m {x_i } } \right) = 2f\left( {\sum\limits_{i = 1}^m {mx_i } } \right)} $ in a large class of complete probabilistic normed spaces, via fixed point theory.

On the stability of some functional equations in Menger φ-normed spaces

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Dorel Miheţ ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
The Stability ◽  
Stability Results

AbstractRecently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

scholarly journals RIEMANN–LIOUVILLE FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH FRACTIONAL NONLOCAL MULTI-POINT BOUNDARY CONDITIONS

Fractals ◽  
2021 ◽  
pp. 2240002
Author(s):  
BASHIR AHMAD ◽  
BADRAH ALGHAMDI ◽  
RAVI P. AGARWAL ◽  
AHMED ALSAEDI
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Weighted Space ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fractional Integrals ◽  
Existence Theory ◽  
Uniqueness Of Solutions

In this paper, we investigate the existence and uniqueness of solutions for Riemann–Liouville fractional integro-differential equations equipped with fractional nonlocal multi-point and strip boundary conditions in the weighted space. The methods of our study include the well-known tools of the fixed point theory, which are commonly applied to establish the existence theory for the initial and boundary value problems after converting them into the fixed point problems. We also discuss the case when the nonlinearity depends on the Riemann–Liouville fractional integrals of the unknown function. Numerical examples illustrating the main results are presented.

scholarly journals C*-Algebra Valued Modular G-Metric Spaces with Applications in Fixed Point Theory

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2003
Author(s):  
Dipankar Das ◽  
Lakshmi Narayan Mishra ◽  
Vishnu Narayan Mishra ◽  
Hamurabi Gamboa Rosales ◽  
Arvind Dhaka ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
C Algebra ◽  
Modular Metric Spaces ◽  
Class Function ◽  
New Type ◽  
The Stability

This article introduces a new type of C*-algebra valued modular G-metric spaces that is more general than both C*-algebra valued modular metric spaces and modular G-metric spaces. Some properties are also discussed with examples. A few common fixed point results in C*-algebra valued modular G-metric spaces are discussed using the “C*-class function”, along with some suitable examples to validate the results. Ulam–Hyers stability is used to check the stability of some fixed point results. As applications, the existence and uniqueness of solutions for a particular problem in dynamical programming and a system of nonlinear integral equations are provided.

scholarly journals The Stability of a General Sextic Functional Equation by Fixed Point Theory

2020 ◽  
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung ◽  
Jaiok Roh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Stability

In this paper, we consider the generalized sextic functional equation \begin{align*} \sum_{i=0}^{7}{}_7 C_{i} (-1)^{7-i}f(x+iy) = 0. \end{align*} And by applying the fixed point theory in the sense of L. C\u adariu and V. Radu, we will discuss the stability of the solutions for this functional equation.

scholarly journals A Fixed Point Approach to the Stability of the Cauchy Additive and Quadratic Type Functional Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Sun Sook Jin ◽  
Yang-Hi Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Approach ◽  
The Stability

We investigate the stability of the functional equation by using the fixed point theory in the sense of Cădariu and Radu.

scholarly journals Existence Theory forq-Antiperiodic Boundary Value Problems of Sequentialq-Fractional Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi ◽  
Hana Al-Hutami
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
Existence Theory ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class ◽  
Nonlinear Alternative ◽  
Banach’S Contraction Principle

We discuss the existence and uniqueness of solutions for a new class of sequentialq-fractional integrodifferential equations withq-antiperiodic boundary conditions. Our results rely on the standard tools of fixed-point theory such as Krasnoselskii's fixed-point theorem, Leray-Schauder nonlinear alternative, and Banach's contraction principle. An illustrative example is also presented.

scholarly journals The Stability of a General Sextic Functional Equation by Fixed Point Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jaiok Roh ◽  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Fixed Point Theorem ◽  
The Stability

In this paper, we will consider the generalized sextic functional equation ∑ i = 0 7   7 C i − 1 7 − i f x + i y = 0 . And by applying the fixed point theorem in the sense of C a ˘ dariu and Radu, we will discuss the stability of the solutions for this functional equation.

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