On completeness of partial metric spaces, symmetric spaces and some fixed point results

The purpose of the thesis is to study completeness of abstract spaces. In particular, we study completeness in partial metric spaces, partial metric type spaces, dislocated metric spaces, dislocated metric type spaces and symmetric spaces that are generalizations of metric spaces. It is well known that complete metric spaces have a wide range of applications. For instance, the classical Banach contraction principle is phrased in the context of complete metric spaces. Analogously, the Banach's xed point theorem and xed point results for Lipschitzian maps are discussed in this context, namely in, partial metric spaces and metric type spaces. Finally, xed point results are presented for symmetric spaces.GeographyPh. D. (Mathematics

On some results of analysis in metric spaces and fuzzy metric spaces

The notion of a fuzzy metric space due to George and Veeramani has many advantages in analysis since many notions and results from classical metric space theory can be extended and generalized to the setting of fuzzy metric spaces, for instance: the notion of completeness, completion of spaces as well as extension of maps. The layout of the dissertation is as follows: Chapter 1 provide the necessary background in the context of metric spaces, while chapter 2 presents some concepts and results from classical metric spaces in the setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy metric spaces, among others we show that: the product of two complete fuzzy metric spaces is also a complete fuzzy metric space. Our main contribution is in chapter 4. We introduce the concept of a standard fuzzy pseudo metric space and present some results on fuzzy metric identification. Furthermore, we discuss some properties of t-nonexpansive maps.Mathematical SciencesM. Sc. (Mathematics

Fixed point theorems for (ε, λ)-uniformly locally contractive mapping defined on ε-chainable G-metric type spaces

In this article, we discuss fixed point results for (ε, λ)-uniformly locally contractive self mapping defined on ε-chainable G-metric type spaces. In particular, we Show that under some more general conditions, certain fixed point results already obtained in the literature remain true

Inertial subgradient extragradient with projection method for solving variational inequality and fixed point problems

In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature

Sensitivity analysis-based control strategies of a mathematical model for reducing marijuana smoking

The aim of the current study is to reduce marijuana use among the general population. Because marijuana is an illegal narcotic with numerous negative health effects, it continues to pose a severe threat to public health in emerging nations. In this article, a modified mathematical model of the non-users, experimental users, recreational users, and addict's (NERA) model for marijuana consumption is established by incorporating a new compartment that represents the individuals who are being moved to jail by police intervention. The overall population of humans is divided into five main components: the non-smoker's compartment, experimental smoker's compartment, recreational smoker's compartment, addicted smoker's compartment, and prisoner's compartment. The novelty of this work is to modify the NERA model for marijuana consumption and validate the modified model. Furthermore, with the help of sensitivity analysis, control strategies for marijuana consumption in the population are addressed. The invariant region and the basic reproductive number (R0) are those parts that are needed for the validation of the proposed model. For the numerical simulation of the given model, the 4th-order Runge Kutta method will be used with the help of MATLAB to examine how the control strategies will play a role in marijuana consumption

W-shaped chirp free and chirped bright, dark solitons for perturbed nonlinear Schrödinger equation in nonlinear optical fibers

In the present investigation, we employed the Jacobi elliptic function (JEF) method to invoke the perturbed nonlinear Schrödinger equation with self-steepening (SS), self-phase modulation (SPM), and group velocity dispersion (GVD), which govern the propagation of solitonic pulses in optical fibres. The proposed algorithm proves the existence of the family of solitons in optical fibers. Consequently, chirped and chirp free W-shaped bright, dark soliton solutions are obtained from dn(ξ), cn(ξ) and sn(ξ) functions. The final results are displayed in three-dimensional plots with specific physical values of GVD, SPM and SS for an optical fiber

An Efficient Parallel Extragradient Method for Systems of Variational Inequalities Involving Fixed Points of Demicontractive Mappings

Herein, we present a new parallel extragradient method for solving systems of variational inequalities and common fixed point problems for demicontractive mappings in real Hilbert spaces. The algorithm determines the next iterate by computing a computationally inexpensive projection onto a sub-level set which is constructed using a convex combination of finite functions and an Armijo line-search procedure. A strong convergence result is proved without the need for the assumption of Lipschitz continuity on the cost operators of the variational inequalities. Finally, some numerical experiments are performed to illustrate the performance of the proposed method

α,BK-Contractions in Bipolar Metric Spaces

In this paper, we introduce the concept of α,BK-contractions and prove the existence of fixed points for contravariant mappings on bipolar metric spaces

Interpolative Kannan Contractions in T0-Quasi-Metric Spaces

In this paper, we update the well-known fixed point theorem of Kannan using the interpolation notion in the realm of quasi-metric spaces. We consider some asymmetric versions. We also present some illustrative examples in support of the obtained results

Halpern-Subgradient Extragradient Method for Solving Equilibrium and Common Fixed Point Problems in Reflexive Banach Spaces

In this paper, using the concept of Bregman distance, we introduce a new Bregman subgradient extragradient method for solving equilibrium and common fixed point problems in a real reflexive Banach space. The algorithm is designed, such that the stepsize is chosen without prior knowledge of the Lipschitz constants. We also prove a strong convergence result for the sequence that is generated by our algorithm under mild conditions. We apply our result to solving variational inequality problems, and finally, we give some numerical examples to illustrate the efficiency and accuracy of the algorithm