Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...

we consider gabor systems generated by a gaussian function and prove certain classical results of paley and wiener on nonharmonic fourier series of complex exponentials for the gabor expansion‎. ‎in particular, we prove a version of plancherel-po ́lya theorem for entire functions with finite order of growth and use the hadamard factorization theorem to study regularity‎, ‎exactness and deficienc...

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

‎The concept of self-similarity on subsets of algebraic varieties‎ ‎is defined by considering algebraic endomorphisms of the variety‎ ‎as `similarity' maps‎. ‎Self-similar fractals are subsets of algebraic varieties‎ ‎which can be written as a finite and disjoint union of‎ ‎`similar' copies‎. ‎Fractals provide a framework in which‎, ‎one can‎ ‎unite some results and conjectures in Diophantine g...

in this paper, vector ultrametric spaces are introduced and a fixed point theorem is given forcorrespondences. our main result generalizes a known theorem in ordinary ultrametric spaces.

‎Let ${X_{alpha}:alphainLambda}$ be a collection of topological spaces‎, ‎and $mathcal {G}_{alpha}$ be a grill on $X_{alpha}$ for each $alphainLambda$‎. ‎We consider Tychonoffrq{}s type Theorem for $X=prod_{alphainLambda}X_{alpha}$ via the above grills and a natural grill on $X$ ‎related to these grills, and present a simple proof to this theorem‎. ‎This immediately yields the classical theorem...

In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metr...

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...