The Stability of the Quartic Functional Equation in Random Normed Spaces

The main problem analyzed in this paper consists in showing that, under some conditions, every almost quartic mapping from a linear space to a random normed space under the Łukasiewicz t-norm can be suitably approximated by a quartic function, which is unique.     

On the Stability of the Functional Equation in Matrix β-Normed Spaces

In this paper we introduce the matrix β-normed space and study the stability of the additive-quadratic type functional equation and the Pexider type functional equation in this type of spaces.     

Approximation of a General Cubic Functional Equation in Felbin’s Type Fuzzy Normed Linear Spaces

In this paper, we investigate the generalized Hyers–Ulam stability of a general cubic functional equation in Felbin’s type fuzzy normed linear spaces and some applications of our results in the stability of general cubic functional equation from a linear space to a Banach space will be exhibited.     

Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces

In this paper we establish the general solution of the functional equation

Stability of Solitary Waves for a Generalized Derivative Nonlinear Schrödinger Equation

We consider a derivative nonlinear Schrödinger equation with a general nonlinearity. This equation has a two-parameter family of solitary wave solutions. We prove orbital stability/instability results that depend on the strength of the nonlinearity and, in some instances, on the velocity. We illustrate these results with numerical simulations.     

The Hyers-Ulam stability of a functional equation deriving from quadratic and cubic functions in quasi-��-normed spaces

In this paper, we investigate the Hyers-Ulam stability of the following function equation 2f（2x ＋ y） ＋ 2f（2x - y） = 4f（x ＋ y） ＋ 4f（x - y） ＋ 4f（2x） ＋ f（2y） - Sf（x） - 8f（y） in quasi-β-normed spaces.     

CQ Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem of Infinite Family of Quasi--asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problems, the set of fixed points of infinite family of quasi- C-asymptotically non-expansive mappings in a Banach space by using the CQ method. Our results improve the main results of Takahashi and Takahashi and Takahashi and Zembayashi. Moreover, the method of proof adopted in the paper is different from that of them.     

Well-Posedness for the Generalized Zakharov–Kuznetsov Equation on Modulation Spaces

We consider the Cauchy problem for the generalized Zakharov–Kuznetzov equation \(\partial _t u + \partial _x \Delta u = \partial _x ( u^{m+1} )\) on two or three space dimensions. We mainly study the two dimensional case and give the local well-posedness and the small data global well-posedness in the modulation space \(M_{2,1}(\mathbb {R}^2)\) for \(m \ge 4\). Moreover, for the quartic case (namely, \(m = 3\)), the local well-posedness in \( M_{2,1}^{1/4}(\mathbb {R}^2)\) is given. The well-posedness on three dimensions is also considered.     

New Generalized R-KKM Type Theorems in General Topological Spaces and Applications

In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.     

Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces

We prove generalized Hyers-Ulam–Rassias stability of the cubic functional equation f(kx+y)+f(kx?y)=k[f(x+y)+f(x?y)]+2(k ³?k)f(x) for all \(k\in \Bbb{N}\) and the quartic functional equation f(kx+y)+f(kx?y)=k ²[f(x+y)+f(x?y)]+2k ²(k ²?1)f(x)?2(k ²?1)f(y) for all \(k\in \Bbb{N}\) in non-Archimedean normed spaces.     

Shrinking Projection Methods for a Family of Quasi-φ-Strict Asymptotically Pseudo-Contractions in Banach Spaces

The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property (K). The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.     

On the General Interpolation Formulas for Discrete Functional Spaces (Ⅰ)

The general interpolation formulas for discrete functional spaces of discrete functions with one index are presented in the note. These are the relationship among the discrete norms in the forms of the summation of powers, the maximum modulo, the Hölder and Lipschitz coefficients for the discrete functions.     

On Liapunov-Razumikhin Theorems for Stability in Functional Differential Equations

For the theory of stability in functional differential equations, Liapunov-Razumikhin method may be the most important one. In § 1 of thin paper, we obtain some Liapunov-Razumikhin theorems for stability of functional differential equations by employing the function V used in the papers [3], [4]. In §2, some simple criteria of asymptotic stability for a class of nonlinear     

On the Cauchy Problem for a Generalized Emden–Fowler-Type Equation

Mathematical Notes -     

Weighted Boundedness for Generalized Maximal andSingular Integral Operators in Orlicz-Morrey Spaces

51.IntroductionTheweightedboundednessformaximalandsingularintegraloperatorsonLp(p>1)andBMofunctionspacesarenowunderstood(see[lj)-AsMorreyspacemaybeconsideredasanextensionofthespaces,itisnaturalandimportanttostudytheweightedbou11dednessformax-imalandsingularintegraloperatorsonMorreyspaces.Thepurposeofthispaperistostu`lythequestion,theweightedboundednessfortheoperatorsinOrlicz-Morreyspacesareobtained,andthecharacterizationsfornon-weightedboundednessofmaximaloperatorarealsoobtained.Someworkint…     

Travelling Wave Solutions for Generalized Fisher Equation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１，２］，ＡｒｏｎｓｏｎａｎｄＷｅｉｎｂｅｒｇｅｒｈａｖｅｓｔｕｄｉｅｄｓｙｓｔｅｍａｔｉｃｌｙｔｈｅｓｃａｌａｒｎｏｎｌｉｎｅａｒｄｉｆｆｕ－ｓｉｏｎｅｑｕａｔｉｏｎｉｎｏｎｅｓｐａｃｅｖａｒｉａｂｌｅｕｔ＝ｕｘｘ＋φ（ｕ），（１．１）ｗｈｅｒｅｕ＝ｕ（ｘ，ｔ）ａｎｄφ（ｕ）ｉｓａｎｏｎｌｉｎｅａｒｆｕｎｃｔｉｏｎ．Ｅｑｕａｔｉｏｎ（１．１）ａｒｉｓｅｓｉｎｓｅｖｅｒａｌａｐｐｌｉｃａ－ｔｉｏｎｓ；Ｓｅｅ［１，２］ａｎｄ［３］ｆｏｒｉｎｆｏｒｍａｔｉｏｎａ…