Yj Cho

Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications

Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mapping from into and a mapping from into with some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalized -Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalized -Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.

Approximately Quintic and Sextic Mappings Form -Divisible Groups into Ŝerstnev Probabilistic Banach Spaces: Fixed Point Method

Using the fixed point method, we investigate the stability of the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients form r-divisible groups into Ŝerstnev probabilistic Banach spaces.

Coupled coincidence point theorems in (intuitionistic) fuzzy normed spaces

In this paper, we prove some coupled coincidence point theorems in fuzzy normed spaces. Our results improve and restate the proof lines of the main results given in the papers (Eshaghi Gordji et al. in Math. Comput. Model. 54:1897-1906, 2011) and (Sintunavarat et al. in Fixed Point Theory Appl. 2011:81, 2011).MSC:47H10, 54H25, 34B15.

Stability of the second order partial differential equations

AbstractWe say that a functional equation (ξ) is stable if any function g satisfying the functional equation (ξ) approximately is near to a true solution of (ξ).In this paper, by using Banachs contraction principle, we prove the stability of nonlinear partial differential equations of the following forms: yx(x,t)=f(x,t,y(x,t)),ayx(x,t)+byt(x,t)=f(x,t,y(x,t)),p(x,t)yxt(x,t)+q(x,t)yt(x,t)+pt(x,t)yx(x,t)-px(x,t)yt(x,t)=f(x,t,y(x,t)),p(x,t)yxx(x,t)+q(x,t)yx(x,t)=f(x,t,y(x,t)).2000 Mathematics Subject Classification. 26D10; 34K20; 39B52; 39B82; 46B99.

A General System of Euler–Lagrange-Type Quadratic Functional Equations in Menger Probabilistic Non-Archimedean 2-Normed Spaces

We prove the generalized Hyers-Ulam-Rassias stability of a general system of Euler-Lagrange-type quadratic functional equations in non-Archimedean 2-normed spaces and Menger probabilistic non-Archimedean-normed spaces.

On Approximate -Ternary -Homomorphisms: A Fixed Point Approach

Using fixed point methods, we prove the stability and superstability of -ternary additive, quadratic, cubic, and quartic homomorphisms in -ternary rings for the functional equation , for each .

Fixed points and stability of functional equations in fuzzy ternary Banach algebras

AbstractBy using Diaz and Margolis fixed point theorem, we establish the generalized Hyers-Ulam-Rassias stability of the ternary homomorphisms and ternary derivations between fuzzy ternary Banach algebras associated to the following (m,n)-Cauchy-Jensen additive functional equation: ∑1≤i1<⋯<im≤n1≤kl≤nkl≠ij,∀j∈{1,…,m}f(∑j=1mxijm+∑l=1n−mxkl)=(n−m+1)n(nm)∑i=1nf(xi).MSC:39B52, 46S40, 26E50.