scholarly journals Characterization and Stability of Multimixed Additive-Quartic Mappings: A Fixed Point Application

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Abasalt Bodaghi ◽  
Idham Arif Alias ◽  
Lida Mousavi ◽  
Sedigheh Hosseini
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Single Equation ◽  
Ulam Stability ◽  
System Of Functional Equations ◽  
Fixed Point Technique ◽  
Quartic Mapping

In this article, we introduce the multi-additive-quartic and the multimixed additive-quartic mappings. We also describe and characterize the structure of such mappings. In other words, we unify the system of functional equations defining a multi-additive-quartic or a multimixed additive-quartic mapping to a single equation. We also show that under what conditions, a multimixed additive-quartic mapping can be multiadditive, multiquartic, and multi-additive-quartic. Moreover, by using a fixed point technique, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations thus generalizing some known results.

Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach

2021 ◽  
Vol 71 (1) ◽  
pp. 117-128
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Single Equation ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
System Of Functional Equations ◽  
Fixed Point Approach ◽  
Quadratic Mappings ◽  
New Form

Abstract In this article, by using a new form of multi-quadratic mapping, we define multi-m-Jensen-quadratic mappings and then unify the system of functional equations defining a multi-m-Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of multi-quadratic and multi-m-Jensen-quadratic functional equations. As a consequence, we show that every multi-m-Jensen-quadratic functional equation (under some conditions) can be hyperstable.

scholarly journals Approximate multi-Jensen-cubic mappings and a fixed point theorem

2020 ◽  
Vol 19 (1) ◽  
pp. 141-154
Author(s):  
Elahe Ramzanpour ◽  
Abasalt Bodaghi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Single Equation ◽  
Ulam Stability ◽  
System Of Functional Equations

AbstractIn this paper, we introduce multi-Jensen-cubic mappings and unify the system of functional equations defining the multi-Jensen-cubic mapping to a single equation. Applying a fixed point theorem, we establish the generalized Hyers-Ulam stability of multi-Jensen-cubic mappings. As a known outcome, we show that every approximate multi-Jensen-cubic mapping can be multi-Jensen-cubic.

scholarly journals Characterization, stability and hyperstability of multi-quadratic–cubic mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abasalt Bodaghi ◽  
Ajda Fošner
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Single Equation ◽  
Ulam Stability ◽  
System Of Functional Equations

AbstractIn this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to a single equation. Applying a fixed point theorem, we study the generalized Hyers–Ulam stability of multi-quadratic–cubic mappings. As a result, we investigate the hyperstability of multi-quadratic–cubic mappings in some senses.

scholarly journals Functional inequalities for generalized multi-quadratic mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Single Equation ◽  
Quadratic Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Several Variables ◽  
Quadratic Mappings ◽  
Stability Results

AbstractIn this article, we introduce some special several variables mappings which are quadratic in each variable and show that such mappings can be defined as a single equation that is the generalized multi-quadratic functional equation. We also apply a fixed point theorem to establish the Hyers–Ulam stability for the generalized multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to some known stability results.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

scholarly journals Common Fixed Point Theorems in Metric Spaces with Applications

2018 ◽  
Vol 11 (4) ◽  
pp. 1177-1190
Author(s):  
Pushpendra Semwal
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
System Of Functional Equations ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper we investigate the existence and uniqueness of common fixed point theorems for certain contractive type of mappings. As an application the existence and uniqueness of common solutions for a system of functional equations arising in dynamic programming are discuss by using the our results.

scholarly journals Hyers-Ulam-Rassias Stability of Some Additive Fuzzy Set-Valued Functional Equations with the Fixed Point Alternative

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yonghong Shen ◽  
Yaoyao Lan ◽  
Wei Chen
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Functional Equations ◽  
Cauchy Type ◽  
Upper Semicontinuous ◽  
Real Separable Banach Space ◽  
Fixed Point Technique ◽  
Supremum Metric ◽  
Stability Results ◽  
Rassias Stability

LetYbe a real separable Banach space and let𝒦CY,d∞be the subspace of all normal fuzzy convex and upper semicontinuous fuzzy sets ofYequipped with the supremum metricd∞. In this paper, we introduce several types of additive fuzzy set-valued functional equations in𝒦CY,d∞. Using the fixed point technique, we discuss the Hyers-Ulam-Rassias stability of three types additive fuzzy set-valued functional equations, that is, the generalized Cauchy type, the Jensen type, and the Cauchy-Jensen type additive fuzzy set-valued functional equations. Our results can be regarded as important extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.

scholarly journals On Walks Avoiding a Quadrant

10.37236/8019 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Kilian Raschel ◽  
Amélie Trotignon
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Single Equation ◽  
Convex Cones ◽  
Symmetric Convex ◽  
System Of Functional Equations ◽  
Quarter Plane ◽  
Discrete Structures ◽  
Linear Transform ◽  
Shortest Queue

Two-dimensional (random) walks in cones are very natural both in combinatorics and probability theory: they are interesting for themselves and also because they are strongly related to other discrete structures. While walks restricted to the first quadrant have been studied a lot, the case of planar, non-convex cones – equivalent to the three-quarter plane after a linear transform – has been approached only recently. In this article we develop an analytic approach to the case of walks in three quadrants. The advantage of this method is to provide uniform treatment in the study of models corresponding to different step sets. After splitting the three quadrants in two symmetric convex cones, the method is composed of three main steps: write a system of functional equations satisfied by the counting generating function, which may be simplified into one single equation under symmetry conditions; transform the functional equation into a boundary value problem; and finally solve this problem, using a concept of anti-Tutte's invariant. The result is a contour-integral expression for the generating function. Such systems of functional equations also appear in queueing theory with the famous Join-the-Shortest-Queue model, which is still an open problem in the non-symmetric case.

A FIXED POINT APPROACH TO THE STABILITY OF GENERAL QUADRATIC EULER-LAGRANGE FUNCTIONAL EQUATIONS IN INTUITIONISTIC FUZZY SPACES

2016 ◽  
pp. 4430-4436
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Fixed Point Approach ◽  
Intuitionistic Fuzzy ◽  
The Stability ◽  
Lagrange Functional ◽  
Intuitionistic Fuzzy Normed Spaces

In this paper, we prove the generalized Hyers-Ulam stability of a general k-quadratic Euler-Lagrange functional equation:for any fixed positive integer in intuitionistic fuzzy normed spaces using a fixed point method.

Study of Fixed Point Theorem for Common Limit Range Property and Application to Functional Equations

2014 ◽  
Vol 52 (1) ◽  
Author(s):  
Hemant Kumar Nashine
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Functional Equations ◽  
Uniqueness Of Solutions ◽  
System Of Functional Equations ◽  
Altering Distance ◽  
Common Limit ◽  
Common Limit Range Property

AbstractThe aim of our paper is to use common limit range property for two pairs of mappings deriving common fixed point results under a generalized altering distance function. Some examples are given to exhibit different type of situation which shows the requirements of conditions of our results. At the end the existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming with the help of a common fixed point theorem is presented.

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