in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.

in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a g...

Recently, many authors have considered the problem of simultaneous lo-calisation and mapping (SLAM). The paper addresses a somewhat diierent problem, that of cooperative localisation and mapping (CLAM). Basically, CLAM involves two or more robots cooperating to build a map of the environment. This cooperation is not aimed at simply increasing the speed with which the map is constructed; rather,...

It is known, that under some natural conditions, the iterates of any continuous mean-type mapping converge to a continuous invariant mean-type mapping, and, moreover, the invariant continuous mean-type mapping is unique. In this paper we show that the assumption of the continuity in the ”moreover” part of this result is superfluous. We also show that every increasing and homogeneous mean is con...

We show that the moments of the trace of a random unitary matrix have combinatorial interpretations in terms of longest increasing subsequences of permutations. To be precise, we show that the 2n-th moment of the trace of a random k-dimensional unitary matrix is equal to the number of permutations of length n with no increasing subsequence of length greater than k. We then generalize this to ot...

Let 〈a1, a2, . . . , an〉 be a sequence of comparable elements. In this paper, we study two constrained versions of the longest increasing subsequence (LIS) problem. The first problem is the range-constrained longest increasing subsequence (RLIS) problem. Given 0 < LI ≤ UI < n and 0 ≤ LV ≤ UV , the objective of the RLIS problem is to deliver a maximum-length increasing subsequence 〈ai1 , ai2 , ....

The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 2 th Catalan number otherwise. We present an involution that proves a refinement of this sign-balance property respecting the length of the longest increasing subsequence of the permutation. In addition, this yields a combinatorial proof of a recent analogous resul...

where Rk,r is the number of permutations of the integers {1, . . . , k} that contain an increasing subsequence of length at least r. Let Xy denote a positive integer valued random variable such that Prob (Xy ≥ r) = F (r; y). If R k,r denotes the complement of Rk,r, i.e. the number of permutations σ ∈ Sk all of whose increasing subsequences have length strictly less than r, then clearly R k,r = ...

expensive to provide these maps  with field measurements  therefore  it is better to use new methods. this study provides a lithological and alteration mapping units with dominant minerals based on hyperspectral images of eo1-hyperion satellite. to do so, two different zones  were  investigated:  the  cuprite-nevada  and  mozahem  volcano  in  iran  which  have suitable conditions for our study...