On Variational Inclusion and Common Fixed Point Problems in q

We introduce a general iterative algorithm for finding a common element of the common fixed-point set of an infinite family of λi-strict pseudocontractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in a q-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under very mild conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in some references to a great extent

Strong and weak convergence theorems for an infinite family of lipschitzian pseudocontraction mappings in banach spaces

Author name used in this publication: H. W. Joseph Lee2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

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

Strong Convergence by a Hybrid Algorithm for Finding a Common Fixed Point of Lipschitz Pseudocontraction and Strict Pseudocontraction in Hilbert Spaces

We prove a strong convergence theorem by using a hybrid algorithm in order to find a common fixed point of Lipschitz pseudocontraction and κ-strict pseudocontraction in Hilbert spaces. Our results extend the recent ones announced by Yao et al. (2009) and many others

On Solutions of Variational Inequality Problems via Iterative Methods

We investigate an algorithm for a common point of fixed points of a finite family of Lipschitz pseudocontractive mappings and solutions of a finite family of γ-inverse strongly accretive mappings. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings

The Hybrid Projection Methods for Pseudocontractive, Nonexpansive Semigroup, and Monotone Mapping

We modify the three-step iterative schemes to prove the strong convergence theorems by using the hybrid projection methods for finding a common element of the set of solutions of fixed points for a pseudocontractive mapping and a nonexpansive semigroup mapping and the set of solutions of a variational inequality problem for a monotone mapping in a Hilbert space under some appropriate control conditions. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings

Hierarchical Fixed Point Problems in Uniformly Smooth Banach Spaces

We propose some relaxed implicit and explicit viscosity approximation methods for hierarchical fixed point problems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These relaxed viscosity approximation methods are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under mild conditions

Iterative algorithms for solutions of nonlinear equations in Banach spaces.

Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF