In the present paper‎, ‎we introduce the concept of generalized multivalued $F$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including Nadler's‎.

In this note we study the fibers of a rational map from an algebraic point of view. We begin by describing two interpretations of the word ‘fiber’. Let S = k[x0, . . . , xn] be a polynomial ring over an infinite field k, I ⊂ S an ideal generated by an r+1-dimensional vector space W of forms of the same degree, and φ the associated rational map P → P = P(W ). We will use this notation throughout...

Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed...

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in [16], [8], [6], [7]. We then apply the equation to show that the generalized Chen’s conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-p...

We find a priori and a posteriori error estimates of the best proximity point for the Picard iteration associated to a cyclic contraction map, which is defined on a uniformly convex Banach space with modulus of convexity of power type.

LetX be a Banach space with dualX∗, and letK be a nonempty subset ofX. A gauge function is a continuous strictly increasing function φ : R → R such that φ 0 0 and limt→∞φ t ∞. The duality mapping Jφ : X → X∗ associated with a gauge function φ is defined by Jφ x : {f ∈ X∗ : 〈x, f〉 ‖x‖‖f‖, ‖f‖ φ ‖x‖ }, x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. In the particular case φ t t, the ...

Let X be a smooth complex projective variety with nef ⋀2TX and dim⁡X≥3. We prove that, up to finite étale cover X˜→X, the Albanese map X˜→Alb(X˜) is locally trivial fibration whose fibers are isomorphic Fano F ⋀2TF. As bi-product, we see that TX or variety. Moreover study contraction of KX-negative extremal ray φ:X→Y. In particular, blow-up space at point if φ birational type. also morphism fib...

The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $m which is generated by a product of disjoint cycles is explicitly given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler φ-function and the Möbius function.

Let A be the Cantor space of bi-infinite sequences in a finite alphabet A, and let σ be the shift map on A. A cellular automaton is a continuous, σ-commuting self-map Φ of A, and a Φ-invariant subshift is a closed, (Φ, σ)-invariant subset S ⊂ A. Suppose a ∈ A is S-admissible everywhere except for some small region we call a defect. It has been empirically observed that such defects persist unde...