Free percolation and seepage flows from watercourses

Free percolation and seepage flows from natural and artificial watercourses with curvilinear profiles are considered. The rigorous hydrodynamic solution of the problem of free percolation and seepage flow from a watercourse is obtained by representing the watercourse profiles in the plane of the Joukowski variable by means of the equation of a family of lemniscates and using the conformal mapping method. The calculated dependences for determining all the necessary parameters of the seepage flows and constructing the curvilinear watercourse profiles are given. In the case of a circular basis for the shape of the watercourse profile in the plane of the Joukowski variable these dependences coincide with the well-known exact dependences.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 94–99. Original Russian Text Copyright © 2004 by Anakhaev.     

On rotationally starlike logharmonic mappings

This paper considers the class of all mappings of the form where h and g are analytic in the unit disk U, normalized by , and such that is logharmonic with respect to an analytic self‐map a of U. A distortion estimate and the radius of starlikeness are obtained for this class. Additionally, a solution to the problem of minimizing the moments of order p over the class is found, as well as an estimate for arclength.     

Existence and uniqueness results for a class of quasi-hemivariational inequalities

In this paper we are concerned with the study of a nonstandard quasi-hemivariational inequality. Using a fixed point theorem for set-valued mappings the existence of at least one solution in bounded closed and convex subsets is established. We also provide sufficient conditions for which our inequality possesses solutions in the case of unbounded sets. Finally, the uniqueness and the stability of the solution are analyzed in a particular case.     

Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type

In this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem, set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which are announced recently. Application of our theorem to solution of equations of Hammerstein-type is of independent interest.     

Convergence analysis for finite family of relatively quasi nonexpansive mappings and systems of equilibrium problems

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of common fixed points of finite family of relatively quasi-nonexpansive mappings and set of common solutions of a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space is proved using the properties of generalized f-projection operator. Our results extend important recent results.     

Fixed point theorems for random pseudo-contractive mappings

Very recently in Fierro et al. (2009) [6], we obtained a general principle to prove the existence of Random Fixed Point Theorems. As a consequence of this, we have been able to obtain various generalizations for pseudo-contractive mappings with rather simple proofs. In addition, while we were deriving these extensions for random operators, some deterministic results arose, which also appear to be new.     

Convergence analysis of modified iterative approaches in geodesic spaces with curvature bounded above

The objective of this article is to establish a new modified iteration process for nonexpansive mappings in complete CAT(κ) spaces. We prove strong and Δ‐convergence theorems of the proposed method in such spaces under some standard conditions. Furthermore, numerical experiments of non‐trivial examples are also provided to show performance and comparison speed of convergence with many previously known methods. Our main result extended and improved the corresponding recent results announced by many researchers.     

Note on the optimal transportation of distributions

We extend our work on the optimal mapping of distributions in three directions: (a) we consider any set-valued mapping, not just diffeomorphisms; (b) we distinguish between weak and strong optimality, and identify strong optimality with cyclic monotonicity; and (c) we prove that, under some restrictions, a weakly optimal mapping has the subgradient property.     

关于sn度量空间的注记

The main purpose of this paper is to establish the mapping relation between metric spaces and sn-metric spaces.