‎In the present paper‎, ‎we prove the stability of the functional equation‎ ‎\[‎ ‎\max\{f((x\circ y)\circ y),f(x)\}=f(x\circ y)+f(y)‎ ‎\]‎ ‎for real valued functions defined on a square-symmetric groupoid‎ ‎with a left unit element‎. ‎As a consequence‎, ‎we obtain the known result about the stability of the equation‎ ‎\[‎ ‎\max\{f(x+y),f(x-y)\}=f(x)+f(y)‎ ‎\]‎ ‎for real valued functions defined on an abelian group‎.

‎In this short note we present a characterization of compact substitution‎ ‎operators on some weighted spaces of continuous functions‎.

‎In this paper‎, ‎we prove the boundedness for some multilinear commutators generated by the pseudo-differential operator and Lipschitz functions‎.

‎This article is devoted to a brief survey of Furuta inequality and its related topics‎. ‎It consists of 4 sections‎: ‎1‎. ‎From L\"owner-Heinz inequality to Furuta inequality‎, ‎2‎. ‎Ando--Hiai inequality‎, ‎3‎. ‎Grand Furuta inequality‎, ‎and 4‎. ‎Chaotic order‎.

‎In this paper‎, ‎we establish some new coupled fixed point theorems in complete metric spaces‎, ‎using a new concept of $F$-invariant set‎. ‎We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point‎. ‎As applications‎, ‎we discuss and adapt the presented results to the setting of partially ordered cone metric spaces‎. ‎The presented results extend and complement some known existence results from the literature‎.

‎In this paper we will characterize the translates of exponential monomials on an arbitrary Sturm--Liouville hypergroup‎.

‎We investigate an Erdös problem on almost quadratic functions on $\Bbb R$‎.

‎We prove the Hyers--Ulam stability of the Lagrange's mean value‎ ‎points and the Hyers--Ulam--Rassias stability of a differential‎ ‎equation derived from the equation defining the Flett's mean‎ ‎value point‎.

‎This paper begins the study of infinite-dimensional‎ ‎modules defined on bicomplex numbers‎. ‎It generalizes‎ ‎a number of results obtained with finite-dimensional‎ ‎bicomplex modules‎. ‎The central concept introduced‎ ‎is the one of a bicomplex Hilbert space‎. ‎Properties‎ ‎of such spaces are obtained through properties of‎ ‎several of their subsets which have the structure of‎ ‎genuine Hilbert spaces‎. ‎In particular‎, ‎we derive the Riesz‎ ‎representation theorem for bicomplex continuous linear‎ ‎functionals and a general version of the bicomplex Schwarz‎ ‎inequality‎. ‎Applications to concepts relevant to quantum‎ ‎mechanics‎, ‎specifically the bicomplex analogue of the quantum‎ ‎harmonic oscillator‎, ‎are pointed out‎.

‎Let $\mathcal A$ be an algebra and let $\delta‎, ‎\varepsilon‎ :‎\mathcal A \to \mathcal A$ be two linear mappings‎. ‎A ($\delta‎, ‎\varepsilon$)-double derivation is a linear mapping $d‎: ‎\mathcal‎ ‎A\rightarrow \mathcal A$ satisfying‎ ‎$d(ab)=d(a)b+ad(b)+\delta(a)\varepsilon(b)+\varepsilon(a)\delta(b)\;(a,b \in \mathcal{A})$‎. ‎We study some algebraic‎ ‎properties of these mappings and give a formula for calculating $d^n(ab)$‎. ‎We show that if $\mathcal A$ is a Banach algebra such that either is semi-simple or every derivation from $\mathcal A$ into any Banach‎ ‎$\mathcal A$-bimodule is continuous then every ($\delta‎, ‎\varepsilon$)-double derivation on $\mathcal A$ is continuous whenever so are $\delta$‎ ‎and $\varepsilon$‎. ‎We also discuss the continuity of $\varepsilon$ when $d$ and $\delta$ are assumed to be continuous‎.

‎Using a Riemann-Lebesgue lemma for the Fourier transform over the class of‎ ‎bounded variation functions that vanish at infinity‎, ‎we prove the‎ ‎Dirichlet--Jordan theorem for functions on this class‎. ‎Our proof is in the‎ ‎Henstock--Kurzweil integral context and is different to that of‎ ‎Riesz-Livingston [Amer‎. ‎Math‎. ‎Monthly 62 (1955)‎, ‎434--437]‎. ‎As consequence‎, ‎we obtain the Dirichlet--Jordan theorem‎ ‎for functions in the intersection of the spaces of bounded variation‎ ‎functions and of Henstock--Kurzweil integrable functions‎. ‎In this‎ ‎intersection there exist functions in $L^{2}(\mathbb{R})\backslash L(\mathbb{%‎ ‎R}).$‎

‎In this paper‎, ‎a new iterative scheme by hybrid method is constructed‎. ‎Strong convergence‎ ‎of the scheme to a common element of the set of fixed points of an infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved‎. ‎Our results extend important recent results‎.

‎Parallel to the concept of quasi-separate continuity‎, ‎we define a notion for quasi-oscillation of a mapping $f‎: ‎X \times Y \to \mathbb{R}$‎. ‎We also introduce a topological game on $X$ to approximate the oscillation of $f$‎. ‎It follows that under suitable conditions‎, ‎every quasi-separately continuous mapping $f‎: ‎X \times Y \to \mathbb{R}$ has the Namioka property‎. ‎An illuminating example is also given‎.