Brian Fisher

Common Fixed Point Theorems in Complex Valued Metric Spaces

We introduce complex valued metric spaces and obtain sufficient conditions for the existence of common fixed points of a pair of mappings satisfying contractive type conditions.

On the distribution

Powers of the distribution have not been defined. In this paper, we use a double neutrix limit to give meaning to the distribution . *

A new integral transform and associated distributions

In this paper, we generalize the concepts of a new integral transform, namely the Sumudu transform, to distributions and study some of their properties. Further, we also apply this transform to solve one-dimensional wave equation having a singularity at the initial conditions.

On a fixed point theorem of Greguš

We consider two selfmaps T and I of a closed convex subset C of a Banach space X which are weakly commuting in X, i.e.‖TIx−ITx‖≤‖Ix−Tx‖   for   any   x   in   X,and satisfy the inequality‖Tx−Ty‖≤a‖Ix−Iy‖

COMMON FIXED POINT THEOREMS FOR COMPATIBLE MAPPINGS

By using a compatibility condition due to Jungck we establish some common fixed point theorems for four mappings on complete and compact metric spaces These results also generalize a theorem of Sharma and Sahu.

A result on the composition of distributions

LetF be a distribution and letf be a locally summable function. The distributionF(f) is defined as the neutrix limit of the sequenceFn(f), whereFn(x) = F(x) * δn(x) andδn(x) is a certain sequence of infinitely differentiable functions converging to the Dirac delta-functionδ(x). The distribution (xr)−s is valuated forr, s = 1,2, ….

Some results on the non-commutative neutrix product of distributions

It is proved that the non-commutative neutrix product of the distributions x −r and x s ln q |x| exists and for r, q=1, 2, …, s=0,±1,±2, … and r−s>1.

On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function

Let F be a distribution in 𝒟′ and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {F n (f(x))} is equal to h(x), where F n (x)=F(x)*δ n (x) for n=1, 2, … and {δ n (x)} is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ(s)[(sinh−1 x +)1/r ] exists and for s=0, 1, 2, … and r=1, 2, …, where M is the smallest integer greater than (s−r 2+1)/r and Further results are also proved.

Fixed point of multivalued mapping in uniform spaces

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.

ON THE FRESNEL INTEGRALS AND THE CONVOLUTION

The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C