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In this paper, we introduce the concept of compatible maps and weakly compatible maps of type (

In this paper, we present a deterministic non-linear mathematical model for the transmission dynamics of HIV and TB co-infection and analyze it in the presence of screening and treatment. The equilibria of the model are computed and stability of these equilibria is discussed. The basic reproduction numbers corresponding to both HIV and TB are found and we show that the disease-free equilibrium is stable only when the basic reproduction numbers for both the diseases are less than one. When both the reproduction numbers are greater than one, the co-infection equilibrium point may exist. The co-infection equilibrium is found to be locally stable whenever it exists. The TB-only and HIV-only equilibria are locally asymptotically stable under some restriction on parameters. We present numerical simulation results to support the analytical findings. We observe that screening with proper counseling of HIV infectives results in a significant reduction of the number of individuals progressing to HIV. Additionally, the screening of TB reduces the infection prevalence of TB disease. The results reported in this paper clearly indicate that proper screening and counseling can check the spread of HIV and TB diseases and effective control strategies can be formulated around 'screening with proper counseling'.

In this paper, employing the common (E.A.) property, we prove a common fixed theorem for weakly compatible mappings via an implicit relation in intuitionistic fuzzy metric space.

In this paper, we introduce a new class of expansive mappings called generalized (ξ , α)-expansive mappings and investigate the existence of a fixed point for the mappings in this class. We conclude that several fixed-point theorems can be considered as a consequence of main results. Moreover, some examples are given to illustrate the usability of the obtained results. MSC: 46T99; 54H25; 47H10; 54E50 Keywords: expansive mapping; complete metric space; fixed point IntroductionFixed-point theory has attracted many mathematicians since it provides a simple proof for the existence and uniqueness of the solutions to various mathematical models (integral and partial differential equations, variational inequalities etc.). After the celebrated results of Banach [], fixed-point theory became one of the most interesting topics in nonlinear analysis. Consequently, a number of the papers have appeared since then; see e.g. +∞ n= ψ n (t) < +∞ for each t > , where ψ n is the nth iterate of ψ .(ii) ψ is non-decreasing. for all x, y ∈ X.