Continuity Of Functions Research Articles

New Kantorovich-type Szász–Mirakjan Operators

In this paper, we present a Kantorovich-type Szász–Mirakjan operators. Initially, we establish the recurrence relationship for the moments of these operators and provide the central moments up to the fourth degree. Subsequently, we analyze the local approximation properties of these operators using Peetre’s K-function. We investigate the rate of convergence, by utilizing the ordinary modulus of continuity and Lipschitz-type maximal functions. Additionally, we prove weighted approximation theorems and Voronoskaja-type theorems specific to these new operators. Following this, we introduce bivariate extension of these operators and investigate some approximation properties. Lastly, we include several numerical illustrative examples.

On approximating properties of blended variant of Kantorovich-Stancu type Lupaş operators

We introduce blended variant of Kantorovich-Stancu type Lupa? operators and study convergence and q-statistical convergence properties using Korovkin theorem. We investigate rate of convergence interms of modulus of continuity, Peetre?s K-functional and Lipschitz functions. Some Direct results and Voronovskaja type theorem are established. Moreover, graphical analysis and error estimations are presented using MATLAB.

Approximating fractional calculus operators with general analytic kernel by Stancu variant of modified Bernstein–Kantorovich operators

The main aim of this paper is to approximate the fractional calculus (FC) operator with general analytic kernel by using auxiliary newly defined linear positive operators. For this purpose, we introduce the Stancu variant of modified Bernstein–Kantorovich operators and investigate their simultaneous approximation properties. Then we construct new operators by means of these auxiliary operators, and based on the obtained results, we prove the main theorems on the approximation of the general FC operators. We also obtain some quantitative estimates for this approximation in terms of modulus of continuity and Lipschitz class functions. Additionally, we exhibit our approximation results for the well‐known FC operators such as Riemann–Liouville integral, Caputo derivative, Prabhakar integral, and Caputo–Prabhakar derivative.

On King type modification of $(p,q)$-Lupas Bernstein operators with improved estimates

This paper aims to modify the $(p,q)$-Lupaş Bernstein operators using King's technique and to establish convergence results of these operators by using of modulus of continuity and Lipschitz class functions. Some approximation results for this new sequence of operators are obtained. It has been shown that the convergence rate of King type modification is better than the $(p,q)$-Lupaş Bernstein operators. King type modification of operators also provide better error estimation within some subinterval of $[0,1]$ in comparison to $(p,q)$-Lupaş Bernstein operators. In the last section, some graphs and tables provided for simulation purposes using MATLAB (R2015a).

Inequalities for Approximation of New Defined Fuzzy Post-Quantum Bernstein Polynomials via Interval-Valued Fuzzy Numbers

In this study, we introduce new defined fuzzy post-quantum Bernstein polynomials and present examples illustrating their existence. We investigate their approximation properties via interval-valued fuzzy numbers. We obtain a fuzzy Korovkin-type approximation result, and we obtain inequalities estimating the rate of fuzzy convergence for these polynomials by means of the fuzzy modulus of continuity and Lipschitz-type fuzzy functions. Lastly, we present a Voronovskaja type asymptotic result for fuzzy post-quantum Bernstein polynomials. The methods in this paper are crucial and symmetric in terms of extending the approximation results of these polynomials from the real function space to the fuzzy function space and the applicability to the other operators.

Real valued - continuous functions rings

The main goal of this present work is to introduce new class of continuous functions called - continuous and use this functions to investigate the characterize of all real valued - continuous functions ring on topological space . Basic properties of – continuous and some significant theorems that related with this type of continuity functions are introduced. Moreover, we will show that the ring of all real valued – continuous functions is isomorphic with where is -dimensional space. The quantity demand and investment in research and development, while the other model focuses on a more realistic relationship between the quantit y demand and the price.

“You are Dead, but You are Not”: Social medium (Facebook) is the message in grieving and continuing bonds

Today, one may no longer alive but his social networking sites (SNS) account will still live on. Empirical studies on death and SNS started since 2004 covering issues on grief, bereavement, mourning, relational continuity functions of SNS, and digital legacy. Majority of them applied content and discourse analyses on SNS messages directed to or related to the deceased. Applying McLuhan’s aphorism medium is the message, researcher focused on the interplay among forms and functions of Facebook (FB) as a medium and message that mediates grief and the bereaved persons who are communicators that decided to grieve on FB. This research adopts grounded theory approach where in- depth interviews with 10 bereaved persons who maintain relational continuity with their deceased loved ones through FB were conducted. The conclusions are drawn to prove that bereaved users preferred to engage in a transcoporeal mediated communication with deceased for continuing bonds due to four main reasons – the deceased are perceived “dead but they are not”; maintaining relational continuity via FB is essential to “finish their unfinished business”; they felt aided and embraced when adopting “FB the Public Platform for Private Grief”, and they imagined a mutual communication based on “past experience and religious belief”. The mediated transcopereal communication (TcC) is enabled because the social medium (FB) is the message.

On Cauchy condition and related notion of connectedness

Connectedness (resp. uniform connectedness [14]) of uniform spaces can be defined in terms of continuous (resp. uniformly continuous) functions to a discrete space requiring that every continuous (resp. uniformly continuous) function to a discrete space has to be constant. Replacing uniformly continuous functions by the strictly weaker notion of Cauchy regular functions [15] we obtain a new notion of connectedness, namely Cauchy connectedness which happens to be an intermediate notion between connectedness and uniform connectedness. We primarily investigate several features of this new notion. Further in metric spaces, we turn our attention to quasi-Cauchy sequences [10] and show that replacing Cauchy regular continuity by ward continuity (functions preserving quasi-Cauchy sequences, see [11]) one again gets back the notion of uniform connectedness. Finally we define WC spaces in line of UC spaces and obtain certain characterizations.

Bivariate Dunkl Analogue of Stancu Type q-Szász–Mirakjan–Kantorovich Operators and Rate of Convergence

In the present paper, we prove some results on rate of convergence for Dunkl analogue of Stancu type q-Szasz–Mirakjan–Kantorovich operators in terms of second-order modulus of continuity and Lipschitz functions. Further, we construct the bivariate extension of these operators and obtain some approximation results.

Generalized Hölder Continuity and Oscillation Functions

We study a notion of generalized Holder continuity for functions on ℝd. We show that for any bounded function f of bounded support and any r > 0, the r-oscillation of f defined as $osc_{r} f (x):= \sup _{B_{r}(x)} f - \inf _{B_{r}(x)} f$ is automatically generalized Holder continuous, and we give an estimate for the appropriate (semi)norm. This is motivated by applications in the theory of dynamical systems.

Approximation Properties of Kantorovich Type Modifications of $(p, q)-$Meyer-König-Zeller Operators

In this paper, we introduce Kantorovich type modification of $(p, q)$-Meyer-König-Zeller operators. We estimate rate of convergence of proposed operators using modulus of continuity and Lipschitz class functions. Further, we obtain the statistical convergence and local approximation results for these operators. In the last section, we estimate the rate of convergence of $(p, q)$-Meyer-König-Zeller Kantorovich operators by means of Matlab programming.

A two-dimensional approach for sound attenuation of multi-chamber perforated resonator and its optimal design

A two-dimensional (2D) method is investigated to predict the acoustic performances of single-chamber perforated reactive resonators. The effect of non-planar wave propagation on the acoustic performance of acoustically short and long resonator is studied. A desirable resonance behavior appears in acoustically short chamber substantially below the cut-off frequency due to non-planar wave propagation. Adding inlet/outlet extensions has similar effects to that of reducing perforation rate on acoustic performances for short-length perforated resonators. Based on the 2D approach, a 2D transfer matrix method (TMM) is developed through solving the acoustical continuity functions under two outlet boundary conditions to predict the acoustic performances of multi-chamber perforated resonators (MCPRs) which can attenuate broadband noise. Comparisons between the calculations and tests show that the 2D TMM is much more accurate than one-dimensional approach within entire frequency range. In order to evaluate its engineering applicability, a new optimization procedure including a targeted transmission loss curve and a reasonable objective function is introduced to optimize the structure parameters of a MCPR with three chambers using a genetic algorithm. The result can meet the target well at desired frequencies under space constraint. The theoretical method developed in this work can be used for the calculation and optimization of MCPRs in various applications.

Modified Stancu type Dunkl generalization of Szász–Kantorovich operators

In this paper, we introduce a modification of the Szasz–Mirakjan–Kantorovich operators as well as Stancu operators (or a Dunkl generalization of modified Szasz–Mirakjan–Kantrovich operators) which preserve the linearity. This type of modification enables better error estimation on the interval $$[1/2,\infty )$$ rather than the classical Dunkl Szasz–Mirakjan–Kantrovich as well as Stancu operators. We obtain some approximation results via well known Korovkin’s type theorem. We also calculate the rate of convergence of operators by means of modulus of continuity and Lipschitz type maximal functions.

Almost contra βθ -continuity in topological spaces

Abstract In this paper, we introduce and investigate the notion of almost contra βθ -continuous functions by utilizing βθ -closed sets. We obtain fundamental properties of almost contra βθ -continuous functions and discuss the relationships between almost contra βθ -continuity and other related functions.

The Observation Of Defects Of School Buildings Over 100 Years Old In Perak

Malaysia is blessed with a rich legacy of heritage buildings with unique architectural and historical values. The heritage buildings become a symbol of the national identity of our country. Therefore, heritage buildings, as important monuments should be conserved well to ensure the extension of the building’s life span and to make sure continuity functions of the building for future generations. The aim of this study is to analyze the types of defects attached in school buildings over 100 years located in Perak. The data were collected in four different schools aged over 100 years in Perak. The finding of the study highlighted the types of defects which were categorized based on building elements, including external wall, roof, door, ceiling, staircase, column, internal wall, floor and windows. Finding showed that the type of defects occurred in school buildings over 100 years in Perak is the same as the other heritage buildings. This finding can be used by all parties to take serious actions in preventing defects from occurring in buildings over 100 years. This would ensure that buildings’ functional life span can be extended for future use.

On Contra $\pi g\gamma$-Continuous Functions

In this paper, we introduce and investigate the notion of contra $\pi g\gamma$-continuous functions by utilizing $\pi g\gamma$-closed sets [31]. We obtain fundamental properties of contra $\pi g\gamma$-continuous functions and discuss the relationships between contra $\pi g\gamma$-continuity and other related functions.

Penganekaragaman dan Penyeragaman dalam Aktivitas Nelayan Pulau Sembilan: Sebuah Penjelasan Prosesual dan Kontekstual

This article describes and explains the complexity of dynamic process of sea fishery in Pulau Sembilan since the ancient up to now. With the application of the concepts such as diverging, homogenizing, continuity, and temporal, it has been found that the complexity of dynamic process of the fishing economy has oscillated between divergence and homogeneity. The divergence refers to different kinds of fishing activities based on various fish species by different traditional catch techniques, on the other hand, homogeneity refers to the concentration of fishermen activities on one or more similar kinds of fishing activities such as catching life fish (kerapu, sunu, napoleon) and life lobster as top commodities in the period of 1990s. When the populations of the main fish species were decreased as negative impact of overexploitation since the beginning of the 2000s, there were many fishermen returning again to different kinds of fishing activities. It means that the diverging process began its era. The process of diverging and homogenizing of fishery involve cognitive systems as guide for fishermen decision making. These processes indicate persistent and temporal functions of traditional and new fishing techniques of Pulau Sembilan fishing communities. By processual and contextual explanation, it was clear that diverging and homogenizing of fishery is a continuum of its dynamic process. The processes are influenced by internal and external socio-cultural factors and the change of sea physical environment and natural resource conditions. From this explanation known that new practice of using potassium cyanide contributes significantly to the serious degradation of large part of coral reef zones in and outside of Pulau Sembilan water. Key words: Coral reef resource use, diverging and homogenizing, continuity and temporal functions.

On classes of M.K. Potapov

Estimates for modulus of continuity functions, that are integrable on the segment, are obtained.

Ionization parameters of high power microwave flashover on dielectric window surface calculated by particle-in-cell simulation for fluid modeling

The particle-in-cell (PIC) simulation method is used to get the reliable ionization parameters of high power microwave flashover and breakdown on dielectric surface for fluid modeling. Firstly, the PIC method is presented briefly, including dynamic equations, secondary emission and Monte-Carlo collision (MCC) between electron and gas atom. Secondary, the fluid global model (GM) is introduced including continuity and energy conservation functions. Finally, by using a 1D3V PIC-MCC code programmed by the authors, the ionization parameters are calculated under different microwave electric-field values, microwave frequencies, gas types and pressures for fluid modeling, including ionization frequency, breakdown delay time, average electron energy, electron energy distribution function (EEDF). The numerical results could be concluded as follows. Average electron energy is unrelated to EEDF type. At middle and low gas pressures, electron energy satisfies Maxwell distribution, and ionization parameters are unrelated to EEDF type. At middle and high gas pressures, ionization parameter is related to EEDF type, and the relevant coefficient X of EEDF tends to be of high older. Different gases have different EEDF types, and the relevant coefficient X of EEDF should be corrected by PIC simulation. The value of X is also related to microwave electric-field value and frequency, and its value increases with the increase of microwave electric-field value and the decrease of microwave frequency. In a fixed range (microwave electric-field value below 7 MV/m, and microwave frequency below 40 GHz), at middle and low gas pressures, the average electron energy increases with the increase of electric-field value and the decrease of microwave frequency rapidly, and the ionization frequency increases and then decreases with the increase of microwave electric-field value and frequency respectively; at high gas pressure, the average electron energy increases with the increase of electric-field value slowly, the ionization frequency increases with the increase of electric-field value, and the average electron energy and ionization frequency are unrelated to microwave frequency.

EXPLORING THE VALIDITY AND PREDICTIVE POWER OF AN EXTENDED VOLUNTEER FUNCTIONS INVENTORY WITHIN THE CONTEXT OF EPISODIC SKILLED VOLUNTEERING BY RETIREES

The current study examined the structure of the volunteer functions inventory within a sample of older individuals (N = 187). The career items were replaced with items examining the concept of continuity of work, a potentially more useful and relevant concept for this population. Factor analysis supported a four factor solution, with values, social and continuity emerging as single factors and enhancement and protective items loading together on a single factor. Understanding items did not load highly on any factor. The values and continuity functions were the only dimensions to emerge as predictors of intention to volunteer. This research has important implications for understanding the motivation of older adults to engage in contemporary volunteering settings.