Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. The p-adic norm is normalized so that |p|p 1/p. Let N be the set of natural numbers and Z N ∪ {0}. Let UD Zp be the space of uniformly differentiable functions on Zp. For f ∈ ...

Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti : K → E, i = 1, . . . ,r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed poin...

For the fast diffusion equation in the mass preserving parameter range, we obtain sharp asymptotic convergence rates to the Barenblatt solution with respect to the relative L∞ norm from spectral gaps by establishing a nonlinear differentiable semiflow in Hölder spaces on a Riemannian manifold called cigar manifold. On this manifold, the equation becomes uniformly parabolic. It is possible to ob...

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and N = N ∪ {0}. The p-adic norm is normally defined by |p|p = 1/p. As an indeterminate, we assume that q ∈ Cp with |1 − q|p < 1 (see [1-43]...

We characterize the three-dimensional spaces admitting at least six or at least seven equidistant points. In particular, we show the existence of C∞ norms on R admitting six equidistant points, which refutes a conjecture of Lawlor and Morgan (1994, Pacific J. Math 166, 55–83), and gives the existence of energy-minimizing cones with six regions for certain uniformly convex norms on R. On the oth...

Let F (u) = h be an operator equation in a Banach space X with Gateaux differentiable norm, ‖F ′(u) − F ′(v)‖ ≤ ω(‖u − v‖), where ω ∈ C([0,∞)), ω(0) = 0, ω(r) is strictly growing on [0,∞). Denote A(u) := F ′(u), where F ′(u) is the Fréchet derivative of F , and Aa := A + aI. Assume that (*) ‖A−1 a (u)‖ ≤ c1 |a|b , |a| > 0, b > 0, a ∈ L. Here a may be a complex number, and L is a smooth path on ...

some algorithms for nding common xed point of a family of mappings isconstructed. indeed, let c be a nonempty closed convex subset of a uniformlyconvex banach space x whose norm is gateaux dierentiable and let {tn} bea family of self-mappings on c such that the set of all common fixed pointsof {tn} is nonempty. we construct a sequence {xn} generated by the hybridmethod and also we give the ...

Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f : K → K a contractive mapping and T : K → K be a uniformly continuous pseudocontractive mapping with F T / ∅. Let {λn} ⊂ 0, 1/2 be a seq...