scholarly journals Some hyperstability results of a p-radical functional equation related to Drygas mappings in non-Archimedean Banach spaces

2021 ◽  
Vol 40 (1) ◽  
pp. 153-174
Author(s):  
Mustapha Esseghyr Hryrou ◽  
Ahmed Nuino ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Natural Number ◽  
Banach Spaces ◽  
Point Theorem ◽  
Radical Functional Equation

The aim of this paper is to introduce and solve the following pradical functional equation related to Drygas mappings f(√(p&x^p+ y^p ))+f(√(p&x^p+ y^p ))=2f(x)+f(y)+f(-y),x,y ∈R, where f is a mapping from R into a vector space X and p ≥ 3 is an odd natural number. Using an analogue version of Brzdȩk’s fixed point theorem [14], we establish some hyperstability results for the considered equation in non-Archimedean Banach spaces. Also, we give some hyperstability results for the inhomogeneous p-radical functional equation related to Drygas mappings f(√(p&x^p+ y^p ))+f(√(p&x^p+ y^p ))=2f(x)+f(y)+f(-y)+G(x,y)

scholarly journals Some hyperstability results of a p-radical functional equation related to quartic mappings in non-archimedean Banach spaces

2021 ◽  
Author(s):  
Ahmed Nuino ◽  
Mustapha Esseghyr Hryrou ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Natural Number ◽  
Banach Spaces ◽  
Point Theorem ◽  
Radical Functional Equation ◽  
Quartic Mapping

The aim of this paper is to introduce and solve the following p-radical functional equation related to quartic mappings. where f is a mapping from R into a vector space X and p ≥ 3 is an odd natural number. Using an analogue version of Brzd¸ek’s fixed point theorem [13], we establish some hyperstability results for the considered equation in non-Archimedean Banach spaces. Also, we give some hyperstability results for the inhomogeneous p-radical functional equation related to quartic mapping.

scholarly journals A New Fixed Point Theorem and a New Generalized Hyers-Ulam-Rassias Stability in Incomplete Normed Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1117
Author(s):  
Maryam Ramezani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Rassias Stability

In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous results.

scholarly journals Brzdęk’s fixed point method for the generalised hyperstability of bi-Jensen functional equation in (2,β)-Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4897-4910
Author(s):  
Iz-Iddine El-Fassi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Point Method ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Fixed Point Theorem

Using the fixed point theorem [12, Theorem 1] in (2,?)-Banach spaces, we prove the generalized hyperstability results of the bi-Jensen functional equation 4f(x + z/2; y + w/2) = f (x,y) + f (x,w) + f (z,y) + f (y,w). Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. The method we use here can be applied to various similar equations in many variables.

scholarly journals On Hyperstability of the Cauchy Functional Equation in n-Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1886
Author(s):  
Janusz Brzdęk ◽  
El-sayed El-hady
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Main Tool ◽  
Normed Spaces ◽  
Cauchy Functional Equation ◽  
Additive Cauchy Functional Equation

We present some hyperstability results for the well-known additive Cauchy functional equation f(x+y)=f(x)+f(y) in n-normed spaces, which correspond to several analogous outcomes proved for some other spaces. The main tool is a recent fixed-point theorem.

Simulation functions and Meir–Keeler condensing operators with application to integral equations

2021 ◽  
Author(s):  
Moosa Gabeleh ◽  
Mehdi Asadi ◽  
Pradip Ramesh Patle
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Darbo’S Fixed Point Theorem ◽  
Simulation Functions ◽  
Condensing Operators

We propose a new concept of condensing operators by using a notion of measure of non-compactness in the setting of Banach spaces and establish a new generalization of Darbo’s fixed point theorem. We also show the applicability of our results to integral equations. A concrete example will be presented to support the application part.

Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

2018 ◽  
Vol 27 (1) ◽  
pp. 37-48
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
LASZLO BALOG ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Condition

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

A FIXED POINT THEOREM IN BANACH SPACES OVER TOPOLOGICAL SEMIFIELDS AND AN APPLICATION

1999 ◽  
Vol 32 (1) ◽  
Author(s):  
H. K. Pathak ◽  
V. V. S. N. Lakshmi ◽  
Kenan Taş ◽  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem
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