In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. particular, generalized existing results a pair of mappings that possess but not continuous at point. We can apply result both discontinuous mappings. concluded our by providing an illustrative example each case application to existence uniqueness solution nonlinear Volterra i...

There exists extensive literature on fixed points of self-mappings in metric and Banach spaces. But in many applications the mappings under examination may not always be self-mappings, therefore fixed point theorems for nonself-mappings form a natural subject for investigation. Assad and Kirk [2] initiated the study of fixed point of nonselfmappings in metrically convex spaces. Indeed while doi...

The purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities V ID(C, I−f) involving nonexpansive type mappings in smooth Banach spaces. We study existence of solutions of variational inequalities V ID(C, I− f) when D is the set of solutions of zeros of accretive operators or the set of fixed points of non...

In this paper, by the Chebyshev-type inequalities we define three mappings, investigate their main properties, give some refinements for Chebyshev-type inequalities, obtain some applications.

Complex dynamics deals with the iteration of holomorphic functions. As is well known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials, which produced beautiful computer generated pictures of Julia sets and the Mandelbrot set. In the same spirit, this article aims to study the dynamics of the simplest non-trivial quasiregular mappings. These are mappi...

Using an analogy of the Lattès’ construction of chaotic rational functions, we show that there are uniformly quasiregular mappings of the nsphere R whose Julia set is the whole sphere. Moreover there are analogues of power mappings, uniformly quasiregular mappings whose Julia set is Sn−1 and its complement in Sn consists of two superattracting basins. In the chaotic case we study the invariant ...