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 In this paper, we discuss the Hyers-Ulam stability, Ulam-Gavruta-Rassias stability, the extended Ulam stability and Refined Ulam stability problems for the Generalized Reciprocal Functional equation (or GRF equation) in several variables.
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.
In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional ... more In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional integral equations by employing the fixed point technique.
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 In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation 4[f(x + 3y) + f(3x + y)] − 9f(x + y) + 15f(x − y) = 4f(3x) + 10f(x) + 9f(3y) − 35f(y) in non-Archimedean elds.
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.
In this paper, using fixed point method we prove the generalized Hyers Ulam Rassias stability of ... more In this paper, using fixed point method we prove the generalized Hyers Ulam Rassias stability of the additive cubic functional equation f(x-ky)=k 2 [f(x+y)+ f(x-y)]+2(1- k 2 )f(x) for fixed integers k, with k≠0,±1 in paranormed spaces.
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 In this paper, we discuss the Hyers-Ulam stability, Ulam-Gavruta-Rassias stability, the extended Ulam stability and Refined Ulam stability problems for the Generalized Reciprocal Functional equation (or GRF equation) in several variables.
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.
In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional ... more In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional integral equations by employing the fixed point technique.
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 In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation 4[f(x + 3y) + f(3x + y)] − 9f(x + y) + 15f(x − y) = 4f(3x) + 10f(x) + 9f(3y) − 35f(y) in non-Archimedean elds.
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.
In this paper, using fixed point method we prove the generalized Hyers Ulam Rassias stability of ... more In this paper, using fixed point method we prove the generalized Hyers Ulam Rassias stability of the additive cubic functional equation f(x-ky)=k 2 [f(x+y)+ f(x-y)]+2(1- k 2 )f(x) for fixed integers k, with k≠0,±1 in paranormed spaces.
Third Issue (F . D . E.) consisting of 9 research papers, 146 pages long, contains various parts ... more Third Issue (F . D . E.) consisting of 9 research papers, 146 pages long, contains various parts of Functional and Differential Equations, namely: Iterative method for singular Sturm - Liouville problems, Euler type boundary value problems in quantum mechanics, positive solutions of boundary value problems, controllability of impulsive functional semi-linear differential inclusions in Frechet spaces, asymptotic properties of solutions of the Emden-Fowler equation, comparison theorems for perturbed half-linear Euler differential equations, almost sure asymptotic estimations for solutions of stochastic differential delay equations, difference equations inspired by Euler’s discretization method, extended oligopoly models.
Second Issue (MT. PDE) consisting of 9 research papers, 117 pages long, contains various parts of... more Second Issue (MT. PDE) consisting of 9 research papers, 117 pages long, contains various parts of
Mixed Type Partial Differential Equations,
namely:
Tricomi - Protter problem of nD mixed type partial differential equations, solutions of generalized
Rassias’ equation, degenerated elliptic equations, mixed type oblique derivative problem, Cauchy
problem for Euler – Poisson - Darboux equation, non - local boundary value problems, nonuniqueness
of transonic flow past a flattened airfoil, multiplier methods for mixed type equations.
First Issue (F. E. I.) consisting of 14 research papers, 181 pages long, contains various parts o... more First Issue (F. E. I.) consisting of 14 research papers, 181 pages long, contains various parts of Functional Equations and Inequalities, namely: Euler’s Life and Work, Ulam stability, Hyers – Ulam stability and Ulam – Gavruta - Rassias stability of functional equations, Euler – Lagrange type and Euler – Lagrange – Rassias quadratic mappings in Banach and Hilbert spaces, Aleksandrov and isometry Ulam stability problems, stability of Pexider and Drygas functional equations, alternative of fixed point, and Hyers - Ulam stability of differential equations.
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Papers by John M Rassias
Functional and Differential Equations,
namely:
Iterative method for singular Sturm - Liouville problems, Euler type boundary value problems in
quantum mechanics, positive solutions of boundary value problems, controllability of impulsive
functional semi-linear differential inclusions in Frechet spaces, asymptotic properties of solutions of
the Emden-Fowler equation, comparison theorems for perturbed half-linear Euler differential
equations, almost sure asymptotic estimations for solutions of stochastic differential delay equations,
difference equations inspired by Euler’s discretization method, extended oligopoly models.
Mixed Type Partial Differential Equations,
namely:
Tricomi - Protter problem of nD mixed type partial differential equations, solutions of generalized
Rassias’ equation, degenerated elliptic equations, mixed type oblique derivative problem, Cauchy
problem for Euler – Poisson - Darboux equation, non - local boundary value problems, nonuniqueness
of transonic flow past a flattened airfoil, multiplier methods for mixed type equations.
Functional Equations and Inequalities,
namely:
Euler’s Life and Work, Ulam stability, Hyers – Ulam stability and Ulam – Gavruta - Rassias stability of
functional equations, Euler – Lagrange type and Euler – Lagrange – Rassias quadratic mappings in
Banach and Hilbert spaces, Aleksandrov and isometry Ulam stability problems, stability of Pexider
and Drygas functional equations, alternative of fixed point, and Hyers - Ulam stability of differential
equations.