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A comprehensive mathematical model is proposed to study two strains of dengue virus with saturated incidence rates and quarantine measures. Imperfect dengue vaccination is also assumed in the model. Existence, uniqueness and stability of the proposed model are proved using the results from fixed point and degree theory. Additionally, well constructed Lyapunov function candidates are also applied to prove the global stability of infection-free equilibria. It is also demonstrated that the model is generalized Ulam-Hyers stable under some appropriate conditions. The model is fitted to the real data of dengue epidemic taken from the city of Espirito Santo in Brazil. For the approximate solution of the model, a non-standard finite difference(NSFD) approach is applied. Sensitivity analysis is also carried out to show the influence of different parameters involved in the model. The behaviour of the NSFD is also assessed under different denominator functions and it is observed that the choice of the denominator function could influence the solution trajectories. Different scenario analysis are also assessed when the reproduction number is below or above one. Furthermore, simulations are also presented to assess the epidemiological impact of dengue vaccination and quarantine measures for infected individuals. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the sufficient conditions for the existence of attractor of a generalized cyclic iterated function system composed of a complete metric space and a finite collection of generalized cyclic Γ-contraction mappings. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an extended rectangular fuzzy b-metric space which generalizes rectangular fuzzy b-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy b-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where a Ćirić type contraction was employed. Our main result generalizes some comparable results in rectangular fuzzy b-metric space and rectangular fuzzy metric space. We provide some examples to support the concepts and results presented herein. As an application of our result, we obtain the existence of the solution of the integral equation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish Kelisky-Rivlin type theorem for α-Bernstein-type operators. To achieve this, we first introduce the concept of a generalized JS-contraction type mapping and then we prove a fixed point theorem which is new and first of its kind in the known literature on fixed point theory. The result presented herein generalizes and improves the main result of Altun et al. [Altun, I., Al Arifi, N., Jleli, M., Lashin, A., Samet, B. (2017). A fixed point theorem for JS-contraction type mappings with applications to polynomial approximations. Filomat. 31(15):4969-4978]. [ABSTRACT FROM AUTHOR]

We prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce the concept of Suzuki type multivalued (θ,R)-contraction and we will prove some fixed point results in the setting of a metric space equipped with a binary relation. Our results generalize and extend various comparable results in the existing literature. Examples are provided to support the results proved here. As an application of our results, we obtain a homotopy result, proving the existence of a solution for a second-order differential equation and for a first-order fractional differential equation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce Ciric-Suzuki type quasi-contractive multivalued operators and to obtain the existence of fixed points of such mappings in the framework of b-metric spaces. Some examples are presented to support the results proved herein. We establish a characterization of strong b-metric and b-metric spaces completeness. An asymptotic estimate of a Hausdorff distance between the fixed point sets of two Ciric-Suzuki type quasi-contractive multivalued operators is obtained. As an application of our results, existence and uniqueness of multivalued fractals in the framework of b-metric spaces is proved. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of common fixed points of multivalued Perov type contractionmappings on conemetric space endowed with a graph. An example is presented to support the results proved herein. Our results unify, generalize and complement various known comparable results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of complex valued fuzzy metric spaces. We prove some fixed point results of contractive mappings on complex valued fuzzy metric spaces. Some examples are presented to support the results proved herein. Our results extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, common fixed point for four maps using an implicit contractive condition in a complete metric space is proved. Some periodic point results for such mappings are also obtained. These results extend and generalize several comparable results in the current literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present common fixed point results of set-valued graphic F-contraction mappings on a family of sets endowed with a graph. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of α-dominated multivalued mappings and establish the existence of common fixed points of such mappings on a closed ball contained in left/right K-sequentially complete dislocated quasi b-metric spaces. These results improve, generalize, extend, unify, and complement various comparable results in the existing literature. Our results not only extend some primary results to left/right K-sequentially dislocated quasi b-metric spaces but also restrict the contractive conditions on a closed ball only. Some examples are presented to support the results proved herein. Finally as an application, we obtain some common fixed point results for single-valued mappings by an application of the corresponding results for multivalued mappings satisfying the contractive conditions more general than Banach type and Kannan type contractive conditions on closed balls in a left K-sequentially complete dislocated quasi b-metric space endowed with an arbitrary binary relation. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate some convergence theorems in fixed point theory for ρ--quasi-nonexpansive multivalued mappings in modular function spaces using a faster iterative process. Examples are provided to validate our results. [ABSTRACT FROM AUTHOR]

In this paper, sufficient conditions for the existence of a commonfixed point for a Banach operator pair of mappings satisfying generalized contractive conditions in the frame work of CAT(0) spaces are obtained. As an application, related results on best approximation are derived. Our results generalize various known results in contemporary literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce Picard-Krasnoselskii hybrid iterative process which is a hybrid of Picard and Krasnoselskii iterative processes. In case of contractive nonlinear operators, our iterative scheme converges faster than all of Picard, Mann, Krasnoselskii and Ishikawa iterative processes in the sense of Berinde (Iterative approximation of fixed points, 2002). We support our analytic proofs with a numerical example. Using this iterative process, we also find the solution of delay differential equation. [ABSTRACT FROM AUTHOR]

We obtain Edelstein-Suzuki type theorems for multivalued mappings in compact b-metric spaces. Moreover, we prove the Bexistence of coincidence and common fixed points of a hybrid pair of mappings that satisfies Edelstein-Suzuki type contractive condition. We present some examples along with a comparison with results in existing literature. In the end, we present some corollaries in the metric spaces with applications in best approximation theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new contraction called dualistic contraction of rational type and used it to obtain some fixed point results in ordered dualistic partial metric spaces. These results generalize various comparable results appeared in the literature. We provide an example to show the usefulness of our results among corresponding fi xed point results proved in metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iteration process and prove the convergence of this iteration process to a fixed point of contractive-like operators. We also present a data dependence result for such mappings. Our results unify and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of cyclic R-contraction mapping and then study the existence of fixed points for such mappings in the framework of metric spaces. Examples and application are presented to support the main result. Our result unify, complement, and generalize various comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

Recently Abbas [M. Abbas, Fixed Point Theory, 13 (2012), 3-10] introduced the concept of f-almost contraction which in turn extended the class of multivalued almost contraction mapping and obtained coincidence point results for this new class of mappings. The aim of this paper is to introduce the notion of dynamic process for generalized (f, L)--almost F--contraction mappings and to obtain coincidence and common fixed point results for such process. It is worth mentioning that our results do not rely on the commonly used range inclusion condition. We provide some examples to support our results. As an application of our results, we obtain the existence and uniqueness of solutions of dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of a common fixed point of almost generalized contractions on modular spaces. As an application, we present some fixed and common fixed point results for such mappings on modular spaces endowed with a graph. The existence of fixed and common points of mappings satisfying generalized contractive conditions of integral type is also obtained in such spaces. Some examples are presented to support the results obtained herein. Our results generalize and extend various comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that a soft metric induces a compatible metric on the collection of all soft points of the absolute soft set, when the set of parameters is a finite set. We then show that soft metric extensions of several important fixed point theorems for metric spaces can be directly deduced from comparable existing results. We also present some examples to validate and illustrate our approach. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of common fixed points of multivalued F-contraction mappings on a metric space endowed with a graph. An example is presented to support the results proved herein. Our results unify, generalize and complement various known comparable results in the literature. [ABSTRACT FROM AUTHOR]

We present fixed point results of mappings satisfying generalized contractive conditions in complex valued metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of generalized contractive-type mappings involved in cocyclic representation of a nonempty subset of a complex valued metric space are also obtained. Some examples are also presented to support the results proved herein. These results extend and generalize many results in the existing literature. [ABSTRACT FROM AUTHOR]

We study the convergence of the Prešić type k-step iterative method for a class of operators [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of fixed points for set-valued mappings satisfying certain graph contractions with set-valued domain endowed with a graph. These results unify, generalize, and complement various known comparable results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a class of multivalued mappings satisfying a Suzuki type generalized contractive condition in the framework of fuzzy metric spaces and to present fixed point results for such mappings. Some examples are presented to support the results proved herein. As an application, a common fixed point result for a hybrid pair of single and multivalued mappings is obtained. We show the existence and uniqueness of a common bounded solution of functional equations arising in dynamic programming. Our results generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present common fixed point results of quasi-weak commutative mappings on a closed ball in the framework of multiplicative metric spaces. Example is presented to support the result proved herein. We also study sufficient conditions for the existence of a common solution of multiplicative boundary value problem. Our results extend and improve various recent results in the existing literature. [ABSTRACT FROM AUTHOR]

In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature. [ABSTRACT FROM AUTHOR]

Abstract: We establish some fixed point theorems by introducing two new classes of contractive mappings in Menger PM-spaces. First, we prove our results for an - -type contractive mapping and then for a generalized -type contractive mapping. Some examples and an application to Volterra type integral equation are given to support the obtained results. [Copyright &y& Elsevier]

Coincidence point theorems for hybrid pairs of single valued and multivalued mappings on an arbitrary nonempty set have been proved. As an application of our main result, the existence of common solutions of functional equations arising in dynamic programming are discussed. [ABSTRACT FROM AUTHOR]

The existence of fixed points of single-valued mappings in modular function spaces has been studied by many authors. The approximation of fixed points in such spaces via convergence of an iterative process for single-valued mappings has also been attempted very recently by Dehaish and Kozlowski (Fixed Point Theory Appl. 2012:118, 2012). In this paper, we initiate the study of approximating fixed points by the convergence of a Mann iterative process applied on multivalued ρ-nonexpansive mappings in modular function spaces. Our results also generalize the corresponding results of (Dehaish and Kozlowski in Fixed Point Theory Appl. 2012:118, 2012) to the case of multivalued mappings. [ABSTRACT FROM AUTHOR]

Existence of a fixed point for a fuzzy mapping satisfying a generalized contractive condition is proved. Our result, supported with an example, provide extension as well as substantial improvements of several well known results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present fixed point results of multivalued mappings in the framework of partial metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. As an application of our main result, the existence and uniqueness of bounded solution of functional equations arising in dynamic programming are established. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a $$w^{*}$$ -compatible mappings to obtain coupled coincidence point and coupled common fixed points of nonlinear contractive mappings in partially ordered metric spaces. Our results generalize, extend, unify, enrich and complement various comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In [Numer. Funct. Anal. Optim. 32 (2011), 243-253], Azam, Fisher, and Khan introduced a notion of complex-valued metric spaces and obtained common fixed point results for mappings satisfying rational inequalities. In the present paper, employing the concept of asymptotically regular mappings, the existence of a fixed point is obtained in a complex-valued metric space. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, using the setting of generalized metric spaces, existence of unique common fixed point of two pairs of power contraction mappings satisfying (E.A)-property in generalized metric spaces is established. We also provide example to support the results presented herein. [Copyright &y& Elsevier]

Abstract: In this paper, we obtain a Suzuki type fixed point theorem for a generalized multivalued mapping on a partial Hausdorff metric space. As a consequence of the presented results, we discuss the existence and uniqueness of the bounded solution of a functional equation arising in dynamic programming. [Copyright &y& Elsevier]

In this paper, we prove some coupled fixed point theorems for contractive mappings in partially ordered complete metric spaces under certain conditions to extend and complement the recent fixed point theorems according to Lakshmikantham and Ćirić [V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70(2009), 4341-4349] and Luong and Thuan [N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74(2011), 983-992]. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we obtained Suzuki type fixed point results for a generalized multi-valued mapping on a set equipped with two b-metrics. As a consequence, existence and uniqueness of solution of functional equation arising in dynamical programming is also derived. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the concept of a partial Hausdorff metric. We initiate study of fixed point theory for multi-valued mappings on partial metric space using the partial Hausdorff metric and prove an analogous to the well-known Nadlerʼs fixed point theorem. Moreover, we give a homotopy result as application of our main result. [Copyright &y& Elsevier]

Abstract: In this paper, using the setting of complete partially orderedG-metric spaces, some common fixed point results of maps that satisfy the generalized -weak contractive condition are obtained. [Copyright &y& Elsevier]

Using the setting of G- metric spaces, some new fixed point theorems for multivalued monotone mappings in ordered G- metric space X are proved, where the partial ordered ≤ in X is obtained by a pair of functions (Ψ, φ). [ABSTRACT FROM AUTHOR]

Abstract: In this paper, using the setting of generalized metric spaces, existence of unique common fixed point is established for mappings satisfying (E.A)-property under generalized strict contractive condition, as well as under some generalized contractions. Obtained results are proper extensions of the existing ones in metric space. We also provide example to support concepts and results presented herein. [Copyright &y& Elsevier]

Fixed point theorems for hybrid pair of single valued and multivalued R-subweakly commuting maps are proved. [ABSTRACT FROM PUBLISHER]

Abstract: The purpose of this paper is to investigate the demiclosedness principle, the existence theorem, and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. Our results generalize, extend and unify the corresponding results of Dhompongsa and Panyanak [S. Dhompongsa, B. Panyanak, On -convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56 (2008) 2572–2579], Osilike and Aniagbosor [M.O. Osilike, S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Computer Model., 32 (2000), 1181–1191], Sahu and Beg [D.R. Sahu, I. Beg, Weak and strong convergence for fixed points of nearly asymptotically non-expansive mappings, Internat. J. Modern Math., 3(2) (2008), 135–151]. [Copyright &y& Elsevier]

We prove some fixed point theorems for a T-Hardy-Rogers contraction in the setting of partially ordered partial metric spaces. We apply our results to study periodic point problems for such mappings. We also provide examples to illustrate the results presented herein. [ABSTRACT FROM AUTHOR]

Recently, Abbas et al. (2012) obtained some unique common fixed-point results for a pair of mappings satisfying (E.A) property under certain generalized strict contractive conditions in the framework of a generalized metric space. In this paper, we present common coincidence and common fixed points of two pairs of mappings when only one pair satisfies (E.A) property in the setup of generalized metric spaces. We present some examples to support our results. We also study well-posedness of common fixed-point problem. [ABSTRACT FROM AUTHOR]

We prove the existence of fixed point of nonexpansive mapping defined on a nonconvex subset of a CAT(0) space. A relationship between fixed point and best approximation is also obtained. [ABSTRACT FROM AUTHOR]