in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

L. Liszkay * , C. Corbel, P Perez DSM/IRFU & IRAMIS, CEA Saclay F-91191 Gif-sur-Yvette Cedex, France P. Desgardin, M.-F. Barthe CNRS-CERI, 3A rue de la Férollerie, F-45071 Orléans Cedex 2, France T. Ohdaira, R. Suzuki AIST, Tsukuba, Ibaraki 305-8568, Japan P. Crivelli, U. Gendotti, A. Rubbia Institut für Teilchenphysik, ETHZ, CH-8093 Zürich, Switzerland M. Etienne, A. Walcarius LCPME, CNRS-Nanc...

In this paper, we prove the generalized Hyers-Ulam(or Hyers-Ulam-Rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$

In this paper, we first introduce some types of generalized $alpha$-Meir-Keeler contractions in $b$-metric-like spaces and then we establish some fixed point results for these types of contractions. Also, we present a new fixed point theorem for a Meir-Keeler contraction through rational expression. Finally, we give some examples to illustrate the usability of the obtained results.

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.

Recently, Suzuki [Nonlinear Anal. 71 (2009), no. 11, 5313–5317.] published a paper on which Edelstein’s fixed theorem was generalized. In this manuscript, we give some theorems which are the generalization of the fixed theorem of Suzuki’s Theorems and thus Edelstein’s result [J. London Math. Soc. 37 (1962), 74-79].

We explicitly determine the structure of Weierstrass semigroups $H(P)$ for any point $P$ Suzuki curve $\mathcal {S}_q$. As varies, exactly two possibilities arise $H(P)$: one $\mathbb {F}_q$-rational points (already kn