Fixed Point Results for an Almost Generalized α -Admissible Z -Contraction in the Setting of Partially Ordered b-Metric Spaces

In this paper, we introduce an almost generalized α -admissible Z -contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a solution of an integral equation.

Advances on the fixed point results via simulation function involving rational terms

In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and unify the existing results in two senses: in the sense of contraction terms and in the sense of the abstract setting. We present an example to indicate the validity of the main theorem.

Common fixed point theorem on Proinov type mappings via simulation function

In this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify the corresponding results in this direction. We also consider an example to indicate the validity of the obtained results.

Modelling of tall-structure lightning return-stroke current using the Electromagnetic Transients Program

The main aim of this PhD work is to advance tall-structure lightning return-stroke current modelling. The Alternative Transients Program (ATP), a version of the Electromagnetic Transients program (EMTP), is used to model the lightning current distribution within a tall structure and the attached lightning channel. The tall structure, namely the CN Tower, is modeled as three or five transmission line sections connected in series. The lightning channel is represented by a transmission line with a continuously expanding length. The presented model takes into account reflections within the tower and within the lightning channel. Locations of reflections, current reflection coefficients and the parameters of the current simulation function are calculated based on the time analysis of the current derivative signal, measured at the tower. The decay parameters of the simulation function are first determined by curve fitting the decaying part of the current obtained from measurement. The other parameters are determined by curve fitting the measured initial current derivative impulse with the derivative of the simulation function, before the arrival of reflections. The simulation results substantially succeeded in reproducing the fine structure of the measured current derivative signal. The model allows for the computation of the lightning current at any point along the current path (the tower and the attached channel), which is required for the calculation of the associated electromagnetic field. Using the three-section model of the tower, the presented return-stroke current model enables the determination of a discrete return-stroke velocity profile, demonstrating that the velocity generally decays with time. Furthermore, based on the five-section model, the proposed approach enables taking into account the existence of upward-connecting leaders, which allowed, for the first time, the determination of upward-connecting leader lengths and return-stroke velocity variation profiles with more details. The return-stroke velocity profile is found to initially increase rapidly with time, reaching a peak, and then decrease less rapidly. The proposed model is also experimentally verified based on the comparison between the computed and measured electromagnetic fields. The simulated electric and magnetic field waveforms are found to reproduce important details of the measured fields, including initial split peaks that appear due to channel-front reflections in the presence of upward-connecting leaders.

Modelling of tall-structure lightning return-stroke current using the Electromagnetic Transients Program

The main aim of this PhD work is to advance tall-structure lightning return-stroke current modelling. The Alternative Transients Program (ATP), a version of the Electromagnetic Transients program (EMTP), is used to model the lightning current distribution within a tall structure and the attached lightning channel. The tall structure, namely the CN Tower, is modeled as three or five transmission line sections connected in series. The lightning channel is represented by a transmission line with a continuously expanding length. The presented model takes into account reflections within the tower and within the lightning channel. Locations of reflections, current reflection coefficients and the parameters of the current simulation function are calculated based on the time analysis of the current derivative signal, measured at the tower. The decay parameters of the simulation function are first determined by curve fitting the decaying part of the current obtained from measurement. The other parameters are determined by curve fitting the measured initial current derivative impulse with the derivative of the simulation function, before the arrival of reflections. The simulation results substantially succeeded in reproducing the fine structure of the measured current derivative signal. The model allows for the computation of the lightning current at any point along the current path (the tower and the attached channel), which is required for the calculation of the associated electromagnetic field. Using the three-section model of the tower, the presented return-stroke current model enables the determination of a discrete return-stroke velocity profile, demonstrating that the velocity generally decays with time. Furthermore, based on the five-section model, the proposed approach enables taking into account the existence of upward-connecting leaders, which allowed, for the first time, the determination of upward-connecting leader lengths and return-stroke velocity variation profiles with more details. The return-stroke velocity profile is found to initially increase rapidly with time, reaching a peak, and then decrease less rapidly. The proposed model is also experimentally verified based on the comparison between the computed and measured electromagnetic fields. The simulated electric and magnetic field waveforms are found to reproduce important details of the measured fields, including initial split peaks that appear due to channel-front reflections in the presence of upward-connecting leaders.

Existence and Uniqueness of Fixed Points of Generalized F-Contraction Mappings

The newest generalization of the Banach contraction through the notions of the generalized F-contraction, simulation function, and admissible function is introduced. The existence and uniqueness of fixed points for a self-mapping on complete metric spaces by the new constructed contraction are investigated. The results of this article can be viewed as an improvement of the main results given in the references.

Remarks on α , β -Admissible Mappings and Fixed Points under Z -Contraction Mappings

In this paper, we discuss about different types of α , β -admissible mappings and introduce some new α , β -contraction-type mappings under simulation function. Furthermore, we present the definition of S -metric-like space and its topological properties. Some fixed point theorems in this space are established, proved, and verified with examples.

Study of Γ-simulation functions, ZΓ-contractions and revisiting the L-contractions

In this paper, we introduce the notions of Z?-ontractions and Suzuki Z?-contractions via ?-simulation functions. By using these new contractions, we extend and unify several existing fixed point results in the corresponding literature. We also show that the recently defined notion of L-simulation function is an special case of Z?-contraction. In addition, some notable examples are given to illustrate and support the obtained results.