‎The proximal point algorithm‎, ‎which is a well-known tool for finding‎ ‎minima of convex functions‎, ‎is generalized from the classical‎ ‎Hilbert space framework into a nonlinear setting‎, ‎namely‎, ‎geodesic‎ ‎metric spaces of nonpositive curvature‎. ‎In this paper we propose an‎  ‎iterative algorithm for finding the common element of the‎ ‎minimizers of a finite family of convex functions a...

In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

In this framework, the effect of a Kerr-like medium and coupling function dependent on number photons operator interaction between two-level atom non-linear field is studied. A relation parameter field-atom used to obtain simplified formula for Rabi frequency. The wave proposed model obtained, followed by derivation phase distribution from which wehrl entropy calculated. initial state func?tion...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

The analysis of flow in water-distribution networks with several pumps by the Content Model may be turned into a non-convex optimization uncertain problem with multiple solutions. Newton-based methods such as GGA are not able to capture a global optimum in these situations. On the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...

Combining modules as rst class data structures with explicit input/output-operations for arbitrary expressions in a purely functional programming language brings the exibility of integrated programming environments under control of the functional language. Compared to conventional module systems, the proposed solution provides enhanced func-tionality in a simpler framework, using the functional...

This paper compares the use of Lisp and Prolog for the implementation of a func tional grammar uni cation system To achieve this comparison we have taken as a starting point Michael Elhadad s FUF system which is written in Lisp and produced a much smaller and more e cient Prolog version PFUF retaining many of FUF s essential features Our approach is based on a precompilation scheme that reduces...