Fractals Generated by Various Iterative Procedures – A Survey

These days fractals and the study of their dynamics is one of the emerging and interesting area for mathematicians. New fractals for various equations have been created using one-step iterative procedure, two-step iterative procedure, three-step iterative procedure and four-step iterative procedure in the literature. Fractals are geometric shapes that have symmetry of scale. In this paper, a detailed survey of fractals existing in the literature such as Julia sets, Mandelbrot sets, Cantor sets, etc have been given

Shadow of operators on frames

Aldroubi introduced two methods for generating frames of a Hilbert space H. In one of his method, one approach is to construct frames for H which are images of a given frame for H under T ∈ B (H, H), a collection of all bounded linear operator on H. The other method uses bounded linear operator on ` 2 to generate frames of H. In this paper, we discuss construction of the retro Banach frames in Hilbert spaces which are images of given frames under bounded linear operators on Hilbert spaces. It is proved that the compact operators generated by a certain type of a retro Banach frame can construct a retro Banach frame for the underlying space. Finally, we discuss a linear block associated with a Schauder frame in Banach spaces.Publisher's Versio

Weakly compatible maps in 2

The aim of this paper is to introduce the concept of weakly compatible maps in 2-non-Archimedean Menger probabilistic metric (PM) spaces and to prove a theorem for these mappings without appeal to continuity. We also provide an application

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

General Common Fixed Point Theorems and Applications

The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of Đorić and Lazović (2011) for a multivalued map on a metric space satisfying Ćirić-Suzuki-type-generalized contraction. Further, as a special case, we obtain a generalization of an important common fixed point theorem of Ćirić (1974). Existence of a common solution for a class of functional equations arising in dynamic programming is also discussed

Property in -Metric Spaces

We prove two general fixed theorems for maps in G-metric spaces and then show that these maps satisfy property P

On the Rate of Convergence of Kirk-Type Iterative Schemes

The purpose of this paper is to introduce Kirk-type new iterative schemes called Kirk-SP and Kirk-CR schemes and to study the convergence of these iterative schemes by employing certain quasi-contractive operators. By taking an example, we will compare Kirk-SP, Kirk-CR, Kirk-Mann, Kirk-Ishikawa, and Kirk-Noor iterative schemes for aforementioned class of operators. Also, using computer programs in C++, we compare the above-mentioned iterative schemes through examples of increasing, decreasing, sublinear, superlinear, and oscillatory functions

Iterative algorithm for solving monotone inclusion and fixed point problem of a finite family of demimetric mappings

The goal of this study is to develop a novel iterative algorithm for approximating the solutions of the monotone inclusion problem and fixed point problem of a finite family of demimetric mappings in the context of a real Hilbert space. The proposed algorithm is based on the inertial extrapolation step strategy and combines forward-backward and Tseng's methods. We introduce a demimetric operator with respect to $M$-norm, where $M$ is a linear, self-adjoint, positive and bounded operator. The algorithm also includes a new step for solving the fixed point problem of demimetric operators with respect to the $M$-norm. We study the strong convergence behavior of our algorithm. Furthermore, we demonstrate the numerical efficiency of our algorithm with the help of an example. The result given in this paper extends and generalizes various existing results in the literature

Identification of a Sudden Cardiac Death Susceptibility Locus at 2q24.2 through Genome-Wide Association in European Ancestry Individuals

Sudden cardiac death (SCD) continues to be one of the leading causes of mortality worldwide, with an annual incidence estimated at 250,000–300,000 in the United States and with the vast majority occurring in the setting of coronary disease. We performed a genome-wide association meta-analysis in 1,283 SCD cases and >20,000 control individuals of European ancestry from 5 studies, with follow-up genotyping in up to 3,119 SCD cases and 11,146 controls from 11 European ancestry studies, and identify the BAZ2B locus as associated with SCD (P = 1.8×10−10). The risk allele, while ancestral, has a frequency of ∼1.4%, suggesting strong negative selection and increases risk for SCD by 1.92–fold per allele (95% CI 1.57–2.34). We also tested the role of 49 SNPs previously implicated in modulating electrocardiographic traits (QRS, QT, and RR intervals). Consistent with epidemiological studies showing increased risk of SCD with prolonged QRS/QT intervals, the interval-prolonging alleles are in aggregate associated with increased risk for SCD (P = 0.006)

and Ashish, On the stability of generalized Cauchy linear functional equations, Int

Abstract We investigate the following generalized Cauchy linear functional equation where a is an arbitrary number and prove the Hyers-Ulam-Rassias stability of the functional equations on Banach spaces. Mathematics Subject Classification: 39B52, 39B82, 39B72, 47H0