John M Rassias

National & Kapodistrian University of Athens, Department of Primary Education, Emeritus

Stanford University, Mathematics, Alumnus

University of California, Berkeley, Mathematics, Alumnus

Aristotle University of Thessaloniki, Mathematics Department, Alumnus

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Papers by John M Rassias

Stability of a Quadratic Functional Equation Originating From Sum of the Medians of a Triangle in Fuzzy Ternary Banach Algebras: Direct and Fixed Point Methods

ABSTRACT

A characterization of inner product spaces

arXiv (Cornell University), Sep 1, 2010

In this paper we present a new criterion on characterization of real inner product spaces. We con... more In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space (X, • ) is for some positive integer k ≥ 2 and all x 1 , . . . , x k ∈ X. Conversely, if (X, • ) is an inner product space, then the equality above holds for all k ≥ 2 and all x 1 , . . . , x k ∈ X

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Fractional Linear Algebra

WORLD SCIENTIFIC eBooks, 1995

General solution and generalized Ulam-Hyers stability of a generalized 3-Dimensional AQCQ functional equation

Malaya journal of matematik, 2017

In this paper, we achieve the general solution and generalized Ulam-Hyers stability of a generali... more In this paper, we achieve the general solution and generalized Ulam-Hyers stability of a generalized 3dimensional AQCQ functional equation f (x + r(y + z)) + f (x − r(y + z)) = r 2 [ f (x + y + z) + f (x − y − z)] + 2 1 − r 2 f (x) + (r 4 −r 2) 12 [ f (2(y + z)) + f (−2(y + z)) − 4 f (y + z) − 4 f (−(y + z))] for all positive integers r with r ≥ 2 in Banach Space using two different methods.

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Ulam Stability of Generalized Reciprocal Functional Equation in Several Variables

International journal of applied mathematics and statistics, Aug 10, 2010

In this paper, we discuss the Hyers-Ulam stability, Ulam-Gavruta-Rassias stability, the extended ... more

A Fixed Point Approach to the Stability of Pexider Quadratic Functional Equation with Involution

Journal of Inequalities and Applications, 2010

We apply the fixed point method to investigate the Hyers-Ulam stability of the Pexider functional... more

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Hyers–Ulam Stability of First Order Differential Equation via Integral Inequality

In this chapter, first we derive a nonlinear integral inequality of Gollwitzer type, and as an ap... more In this chapter, first we derive a nonlinear integral inequality of Gollwitzer type, and as an application we investigate the Hyers–Ulam stability of nonlinear differential equation $$\displaystyle y'(t) =f(t,y(t)),\, t\ge a , $$ where f is a given function. The obtained results are new to the literature.

$Research paper thumbnail of (1812-4922) Ulam-Hyers-Rassias stability for fuzzy fractional integral equations$

(1812-4922) Ulam-Hyers-Rassias stability for fuzzy fractional integral equations

Iranian Journal of Fuzzy Systems, Sep 15, 2019

In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional ... more

$Research paper thumbnail of Ulam-Hyers stability of undecic functional equation in quasi-$\beta$-normed spaces: Fixed point method$

Ulam-Hyers stability of undecic functional equation in quasi-$\beta$-normed spaces: Fixed point method

Tbilisi Mathematical Journal, Dec 1, 2016

In this paper, we acquire the general solution of the undecic functional equation f (x + 6y) − 11... more In this paper, we acquire the general solution of the undecic functional equation f (x + 6y) − 11f (x + 5y) + 55f (x + 4y) − 165f (x + 3y) + 330f (x + 2y) − 462f (x + y) + 462f (x) − 330f (x − y) + 165f (x − 2y) − 55f (x − 3y) + 11f (x − 4y) − f (x − 5y) = 39916800f (y). We also obtain the generalized Ulam-Hyers stability of the above functional equation in quasiβ-normed spaces using fixed point method. Moreover, we investigate the pertinent stabilities of the above functional equation using sum of powers of norms, product of powers of norms and mixed product-sum of powers of norms as upper bounds. We also present a counterexample for non-stability of the above functional equation in singular case.

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$Research paper thumbnail of Stability and non-stability of generalized radical cubic functional equation in quasi-$\beta$-Banach spaces$

Stability and non-stability of generalized radical cubic functional equation in quasi-$\beta$-Banach spaces

Tbilisi Mathematical Journal, Jul 1, 2019

Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces

Mathematics, Jan 10, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more

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On the Stability of the Multi-Dimensional Nonlinear Euler-Lagrange Functional Equation

WORLD SCIENTIFIC eBooks, 1995

Generalized Hyers-Ulam Stability of a Mixed Type Additive-quadratic Functional Equation in non-Archimedean Fields

British Journal of Mathematics & Computer Science, Jan 10, 2016

In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation 4[f... more

Best constant for Ulam stability of first-order h-difference equations with periodic coefficient

arXiv (Cornell University), Apr 6, 2020

We establish the best (minimum) constant for Ulam stability of first-order linear hdifference equ... more We establish the best (minimum) constant for Ulam stability of first-order linear hdifference equations with a periodic coefficient. First, we show Ulam stability and find the Ulam stability constant for a first-order linear equation with a period-two coefficient, and give several examples. In the last section we prove Ulam stability for a periodic coefficient function of arbitrary finite period. Results on the associated first-order perturbed linear equation with periodic coefficient are also included.

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Functional Equations And Inequalities: Solutions And Stability Results

PREFACE: Special Issue on Leonhard Paul Euler’s: Mixed Type Partial Differential Equations

International journal of applied mathematics and statistics, Feb 16, 2007

A characterization of inner product spaces

Tricomi-Protter Problem of nD Mixed Type Equations

International journal of applied mathematics and statistics, Feb 16, 2007

The Tricomi equation was established, in 1923, by F. G. Tricomi (Atti Accad. Naz. Lincei, 14, 133... more The Tricomi equation was established, in 1923, by F. G. Tricomi (Atti Accad. Naz. Lincei, 14, 133-247) who was the pioneer of parabolic elliptic and hyperbolic boundary value problems. In 1953, 1954 and 1955 M. H. Protter (J. Rat. Mech. Anal. : 2, 107-114, 1953 ; 3,435-446, 1954; 4, 721-732, 1955) generalized these problems even further for the Tricomi equation in three dimensions. In 1977 the author (Ph.D. Dissertation, Univ. Cal., Berkeley) generalized these results in n dimensions. In 2004, A. Kuzmin ,Frontiers of Fluid Mechanics (World Sci. Publ., Singapore, 285-295) considered the bifurcation of transonic flow over a flattened airfoil. In 2005, G. Wen (Applicable Analysis, 84(12), 1267-1286) investigated the Tricomi problem for second order linear equations of mixed type with parabolic degeneracy. In this paper we investigate the Tricomi- Protter problem of mixed type equations in n dimensions.

Stabilities of Functional Equations on C*-algebras and Lie C*-algebras

Series on concrete and applicable mathematics, Mar 22, 2017

Ulam–Hyers Stabilities of Functional Equations in Felbin’s Normed Spaces

Series on concrete and applicable mathematics, Mar 22, 2017

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