Proof mining in metric fixed point theory and ergodic theory

In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach spaces.Comment: appeared as OWP 2009-05, Oberwolfach Preprints; 71 page

Strong convergence theorems for two finite families of generalized asymptotically quasi-nonexpansive mappings with applications

In this paper, an implicit iteration process has been proposed for two finite families of generalized asymptotically quasi-nonexpansive mappings and establish some strong convergence theorems in the framework of convex metric spaces. Also, some applications of our result has been given. Our results extend and generalize several results from the current existing literature

Ergodic approximations via matrix regularization approach

AbstractIn this paper we use a matrix approach to approximate solutions of variational inequalities in Hilbert spaces. The methods studied combine new or well-known iterative methods (as the original Mann method) with regularized processes that involve regular matrices in the sense of Toeplitz. We obtain ergodic type results and convergence

Variational inequalities and fixed point problems : a survey

U ovoj disertaciji predstavljena je i razrađena teorija neizrazitog vođenja i održavanja procesa toplinskog komfora u mjernom laboratoriju. Izložen je novi sustavski pristup vođenja s posebnim naglaskom na čovjeka- mjeritelja, koji je sastavni dio regulacijskog kruga Konvencionalnom vođenju procesa održavanja toplinskog komfora predviđena je korekcija u skladu s subjektivnim doživljajem, zadržavajući pri tom referentne vrijednosti unutar intervala dopuštenih standardom. Kao rezultat istraživanja odlučeno je i realizirano da se psihološki doživljaj komfora ugradi primjenom neizrazitog slijeda vođenja. Tijekom istraživanja, za potrebe vođenja toplinskog komfora, izrađen je lingvistički deduktivni model, kojim se opisuju svi eventualni lingvistički zahtjevi za promjenom komfora. Pored ovog modela izrađen je i model toplinske i materijalne akumulacije u promatranom prostoru, kako bi se dokazala mogućnost primjene razvijene teorije za vođenje procesa toplinskog komfora. Važan dio predloženog sustava jest inteligentno mjerilo entalpije, izvedeno na temelju istraživanja termodinamike vlažnog zraka. Zamišljen je i realiziran takav inteligentni mjerni uređaj koji povezuje mjerne podatke o tlaku, temperaturi i vlažnosti zraka u promatranom prostoru, sa zbirkom znanja ugrađenom u mikroračunalo, pa kontinuirano računa trenutačne vrijednosti entalpije. Ovaj rad je novi doprinos u teoriji vođenja toplinskog komfora, koja se do sada zasnivala isključivo na stabilizaciji termodinamičkih varijabli stanja.This work presents new process control theory, applied to maintaining thermal comfort in measurement laboratory. In this system approach to process control, human is an essential part of feedback controller. His subjective feeling of thermal comfort is base for applying fuzzy logic; his linguistic information's about temperature and relative humidity in laboratory substitute measurements of a classic feedback controller. Control decisions are result of fuzzy calculations, and controlled variables must be maintained within limits given by Standard. Linguistic deductive model that describes all possible linguistic demands for thermal comfort changes is developed during the research. Also, mathematical model of heat and material accumulation in a laboratory is developed, to confirm applicability of proposed theory for control of thermal comfort process. Important part of proposed system is an intelligent instrument for enthalpy measurement, developed on basis of humid air thermodynamics research. This intelligent measuring instrument combines pressure, temperature and relative humidity measurement data in a laboratory with knowledge base situated in a microprocessor, and continuously calculates enthalpy. This work presents new contribution to theory of thermal comfort control, which was until now based exclusively on stabilisation of thermodynamic variables