Common fixed point theorems for expansion mappings in various spaces

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc. In the memory of 65^th birthday anniversary of his Father Late Sh. Ram Phool Sharma     

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in (0, π). Two sequences of circle patterns are employed to approximate a given conformal map g and its first derivative. For the domain of g we use embedded circle patterns where all circles have the same radius decreasing to 0 and with uniformly bounded intersection angles. The image circle pattern has the same combinatorics and intersection angles and is determined from boundary conditions (radii or angles) according to the values of g′ (|g′| or arg g′). For quasicrystallic circle patterns the convergence result is strengthened to C ^∞-convergence on compact subsets.      

Banach空间中渐近非扩张映象具误差的强收敛定理

设E是一实的Banach空间,其范数是一致Gteaux可微的;D是E的一非空闭凸子集,设T:D→D是具有序列{k_n}[1,∞),lim_(n→∞) k_n=1的渐近非扩张映象.本文证明了,在一定条件下,由(1.3)和(1.5)式定义的具误差的迭代序列{x_n}强收敛于T的不动点.本文结果也推广和改进了最近一些人的最新结果.     

Minimal surfaces over stars

A JS surface is a minimal graph over a polygonal domain that becomes infinite in magnitude at the domain boundary. Jenkins and Serrin characterized the existence of these minimal graphs in terms of the signs of the boundary values and the side-lengths of the polygon. For a convex polygon, there can be essentially only one JS surface, but a non-convex domain may admit several distinct JS surfaces. We consider two families of JS surfaces corresponding to different boundary values, namely JS₀ and JS₁, over domains in the form of regular stars. We give parameterizations for these surfaces as lifts of harmonic maps, and observe that all previously constructed JS surfaces have been of type JS₀. We give an example of a JS₁ surface that is a new complete embedded minimal surface generalizing Scherk's doubly periodic surface, and show also that the JS₀ surface over a regular convex 2n-gon is the limit of JS₁ surfaces over non-convex stars. Finally we consider the construction of other JS surfaces over stars that belong neither to JS₀ nor to JS₁.     

On lengths of filling closed geodesics of hyperbolic punctured Riemann spheres

Let S be a Riemann sphere with n ≥ 4 points deleted. In this article we investigate certain filling closed geodesics of S and give quantitative common lower bounds for the hyperbolic lengths of those geodesics with respect to any hyperbolic structure on S (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inverse spectral problems for differential pencils on the half-line with turning points

The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points is studied. We establish properties of the spectral characteristics, give a formulation of the inverse problem, prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem.     

FIXED POINT RESULTS ON METRIC-TYPE SPACES

In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.     

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

In this paper, we construct a new Roper-Suffridge extension operator Φr n,β1,,βn(f)(z) = F(z) = ((rf(z1/r)/z1)β1z1,(rf(z1/r)/z1)β2z2,...,(rf(z1/r)/z1)βnzn)',where f is a normalized locally biholomorphic function on the unit disc D, r = sup{|z1| : z =(z1, ···, zn) ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.