Some Fixed Point Theorems for Kannan Mappings

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.

New Coefficient Conditions for Functions Starlike with Respect to Symmetric Points

2000 Mathematics Subject Classification: Primary 30C45, secondary 30C80.

Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.

On Differential Inclusions with Unbounded Right-Hand Side

2000 Mathematics Subject Classification: 58C06, 47H10, 34A60.

Reply: 'Myopic foveoschisis: An ectatic retinopathy, not a schisis'

Full text: We thank Tsilimbaris et al1 for their comments on the appropriateness of the term ‘myopic foveoschisis’ to describe the condition that is characterized by the separation of neural retina layers associated with high myopia and posterior staphyloma. They have proposed the term ‘myopic ectatic retinopathy’ as a more literal and functionally more accurate descriptor of the condition to avoid the use of the word ‘schisis’, which may be misleading because it is also used to describe other conditions where there is separation of neural retina layers without the presence of staphyloma.2 Using the word ‘ectatic’ for this condition would imply that we are fairly certain about the pathogenesis and mechanistic factors that underlie its development and progression. However, this is not the case, unfortunately, as our review of the literature has shown. There are several theories ranging from vitreous traction to sclerosing changes of retinal vessels to progression of staphylomas as possible etiological factors. Therefore, it is likely to be multifactorial in nature—hence the success reported with different procedures that address either the vitreous traction factor using vitrectomy, peel plus tamponade or the scleral ectasia factor using posterior buckling techniques. In the absence of a good understanding of underlying pathogenesis, it is probably best to use purely descriptive names rather than mechanistic terms. The use of descriptive terms, even though similar, do not necessarily cause confusion as long as they are widely accepted as differentiating terminology, for example, postoperative pseudophakic cystoid macular edema (Irvine–Gass syndrome) vs cystoid macular edema associated with posterior uveitis in a phakic patient. The introduction of too many mechanistic or pathogenetic terms in the absence of clear understating of etiology can in fact cause more confusion, for example, serous chorioretinopathy vs central serous retinopathy vs serous choroidopathy. The confinement to broad descriptive terms can enhance communication and reduce confusion without committing to any presumption about etiology until it is better understood. This approach is probably best illustrated by the recent advances in the understanding of mactel21, a condition initially described and classified, using descriptive nomenclature, by Don Gass as bilateral, idiopathic acquired juxtafoveolar telangiectasis (Group2A) and as distinctly different from unilateral, congenital parafoveolar telangiectasis (Group 1A; Gass,3 pp 504–506 vs 127–128). Finally, it is worthy to note that for myopic foveoschisis associated with a staphyloma that is associated with outer layer macular detachment, Don Gass also descriptively included the additional observation (before the advent of OCT) that the retinal profile was concave rather than convex in shape, thereby differentiating it from rhegmatogenous detachments with recruitment of subretinal fluid that is associated with posteriorly located breaks and macular holes in myopic eyes. References 1.Tsilimbaris MK, Vavvas DG, Bechrakis NE. Myopic foveoschisis: an ectatic retinopathy, not aschisis. Eye 2016; 30: 328–329. 2.Powner MB, Gillies MC, Tretiach M, Scott A, Guymer RH, Hageman GS et al. Perifoveal müller cell depletion in a case of macular telangiectasia type 2. Ophthalmology 2010; 117(12): 2407–2416. 3.Gass DM. Stereoscopic Atlas of Macular Diseases: Diagnosis and Treatment, 4th edn. Mosby-Yearbook: St. Louis, 1997.

Cooperation in supply chains: A cooperative game theoretic analysis = Együttműködés ellátási láncokban: Egy kooperatív játékelméleti elemzés

A cikkben a kooperatív játékelmélet fogalmait alkalmazzuk egy ellátási lánc esetében. Az ostorcsapás-hatás elemeit egy beszállító-termelő ellátási láncban ragadjuk meg egy Arrow-Karlin típusú modellben lineáris készletezési és konvex termelési költség mellett. Feltételezzük, hogy mindkét vállalat minimalizálja a fontosabb költségeit. Két működési rendszert hasonlítunk össze: egy hierarchikus döntéshozatali rendszert, amikor először a termelő, majd a beszállító optimalizálja helyzetét, majd egy centralizált (kooperatív) modellt, amikor a vállalatok az együttes költségüket minimalizálják. A kérdés úgy merül fel, hogy a csökkentett ostorcsapás-hatás esetén hogyan osszák meg a részvevők ebben a transzferálható hasznosságú kooperatív játékban. = In this paper we apply cooperative game theory concepts to analyze supply chains. The bullwhip effect in a two-stage supply chain (supplier-manufacturer) in the framework of the Arrow-Karlin model with linear-convex cost functions is considered. It is assumed that both firms minimize their relevant costs, and two cases are examined: the supplier and the manufacturer minimize their relevant costs in a decentralized and in a centralized (cooperative) way. The question of how to share the savings of the decreased bullwhip effect in the centralized (cooperative) model is answered by transferable utility cooperative game theory tools.

The Filippov-Wazewski relaxation theorem revisited

The converse statement of the Filippov-Wazewski relaxation theorem is proven, more precisely, two differential inclusions have the same closure of their solution sets if and only if the right-hand sides have the same convex hull. The idea of the proof is examining the contingent derivatives to the attainable sets.

Transferable Utility Games with Uncertainty

We introduce the concept of a TUU-game, a transferable utility game with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TUgames are convex.

Transferable Utility Games with Uncertainty

We introduce the concept of a TUU-game, a transferableutilitygame with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferableutilitygame. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TU-games are convex.

Solution of the Least Squares Method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima.

Endogenous timing of moves in an asymmetric price-setting duopoly

This paper adds to the growing literature on endogenous timing of decisions in duopolies. We show for a price-setting duopoly game with sufficiently asymmetric and strictly convex cost functions that the less efficient firm moves first while the more efficient moves second with a higher price than the less efficient firm.

Stable sets in one-seller assignment games

We consider von Neumann -- Morgenstern stable sets in assignment games with one seller and many buyers. We prove that a set of imputations is a stable set if and only if it is the graph of a certain type of continuous and monotone function. This characterization enables us to interpret the standards of behavior encompassed by the various stable sets as possible outcomes of well-known auction procedures when groups of buyers may form bidder rings. We also show that the union of all stable sets can be described as the union of convex polytopes all of whose vertices are marginal contribution payoff vectors. Consequently, each stable set is contained in the Weber set. The Shapley value, however, typically falls outside the union of all stable sets.

The kernel is in the least core for permutation games

Permutation games are totally balanced transferable utility cooperative games arising from certain sequencing and re-assignment optimization problems. It is known that for permutation games the bargaining set and the core coincide, consequently, the kernel is a subset of the core. We prove that for permutation games the kernel is contained in the least core, even if the latter is a lower dimensional subset of the core. By means of a 5-player permutation game we demonstrate that, in sense of the lexicographic center procedure leading to the nucleolus, this inclusion result can not be strengthened. Our 5-player permutation game is also an example (of minimum size) for a game with a non-convex kernel.

A Kullback-Leibler relatív entrópia függvény alkalmazása páros összehasonlítás mátrix egy prioritásvektora meghatározására (Applying the Kullback-Leibler relative entropy function for determining priorities for the pairwise comparison matrix)

A dolgozatban a döntéselméletben fontos szerepet játszó páros összehasonlítás mátrix prioritásvektorának meghatározására új megközelítést alkalmazunk. Az A páros összehasonlítás mátrix és a prioritásvektor által definiált B konzisztens mátrix közötti eltérést a Kullback-Leibler relatív entrópia-függvény segítségével mérjük. Ezen eltérés minimalizálása teljesen kitöltött mátrix esetében konvex programozási feladathoz vezet, nem teljesen kitöltött mátrix esetében pedig egy fixpont problémához. Az eltérésfüggvényt minimalizáló prioritásvektor egyben azzal a tulajdonsággal is rendelkezik, hogy az A mátrix elemeinek összege és a B mátrix elemeinek összege közötti különbség éppen az eltérésfüggvény minimumának az n-szerese, ahol n a feladat mérete. Így az eltérésfüggvény minimumának értéke két szempontból is lehet alkalmas az A mátrix inkonzisztenciájának a mérésére. _____ In this paper we apply a new approach for determining a priority vector for the pairwise comparison matrix which plays an important role in Decision Theory. The divergence between the pairwise comparison matrix A and the consistent matrix B defined by the priority vector is measured with the help of the Kullback-Leibler relative entropy function. The minimization of this divergence leads to a convex program in case of a complete matrix, leads to a fixed-point problem in case of an incomplete matrix. The priority vector minimizing the divergence also has the property that the difference of the sums of elements of the matrix A and the matrix B is n times the minimum of the divergence function where n is the dimension of the problem. Thus we developed two reasons for considering the value of the minimum of the divergence as a measure of inconsistency of the matrix A.

Improved stochastic optimization of railway timetables

We present a general model to find the best allocation of a limited amount of supplements (extra minutes added to a timetable in order to reduce delays) on a set of interfering railway lines. By the best allocation, we mean the solution under which the weighted sum of expected delays is minimal. Our aim is to finely adjust an already existing and well-functioning timetable. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, building upon earlier research from the literature. We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We show that our model may be solved using any of the following theoretical frameworks: linear programming, stochastic programming and convex non-linear programming, and present a comparison of these approaches based on a real-life case study. Finally, we introduce stochastic dependency into the model, and present a statistical technique to estimate the model parameters from empirical data.