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In this paper, we extend $ \mathcal{F} $-metric spaces to more general spaces, named generalized $ \mathcal{F} $-metric spaces and establish some fixed point theorems via comparison function, $ F $-contraction, Geraghty contraction and JS-contraction in the setting of generalized $ \mathcal{F} $-metric spaces. Our results generalize many present theorems.

In this paper, we prove some fixed point theorems in the framework of G-metric spaces that cannot be obtained from the existence results in the context of quasi-metric spaces.

In this paper, we consider the following Kirchhoff-type equation:{u∈H1(RN),−(a+b∫RN|∇u|2dx)Δu+V(x)u=(Iα*F(u))f(u)+λg(u),inRN, where a&gt, 0, b≥0, λ&gt, 0, α∈(N−2,N), N≥3, V:RN→R is a potential function and Iα is a Riesz potential of order α∈(N−2,N). Under certain assumptions on V(x), f(u) and g(u), we prove that the equation has at least one nontrivial solution by variational methods.

We study an approximate coincidence point and a common fixed point problem for a hybrid pair of mappings with constraints in Menger PM-spaces, and obtain some new results. We derive interesting consequences of the main results by using the properties of a Menger–Hausdorff metric, and analogous results based on graphs instead of partial orders can be similarly formulated. Moreover, we construct two examples to reveal that the main results are valid, and show that the main results can be used to explore the existence of solutions to a system of nonlinear integral equations.

In this paper, some new theorems for various cyclic contractions are established in Gb-metric spaces to discuss the existence and uniqueness of the solutions for a class of the operator equations, which generalize many known results in corresponding literatures. On the other hand, we introduce the notion of the cyclic α-ψφ-contractive mappings in Gb-metric spaces and establish a new fixed point theorem, which is applied to consider the existence of the solutions of the integral equations and ordinary differential equations. Moreover, some examples are given to support our main results.

The aim of this paper is to propose a new φ -coupled fixed point theorem for a mixed monotone mapping in a metric space, which is taken no account of the continuity of the mapping. To this end, we introduce the notions of φ -coupled fixed point and modified F -control function. Our obtained results are applied to derive some φ -coupled fixed point theorems in partial metric spaces and quasi-metric spaces, respectively. Some applications to matrix equations and integral equations are also presented so as to illustrate our results.

In this paper, we introduce the concepts of cyclic $$\varphi $$ -contractions in Menger PM-spaces and cyclic weak $$\phi $$ -contractions in generalized Menger PM-spaces. Based on these concepts, some fixed point results for cyclic $$\varphi $$ -contractions in Menger PM-spaces are obtained. Furthermore, some fixed point theorems for cyclic weak $$\phi $$ -contractions and cyclic $$\varphi $$ -contractions in generalized Menger PM-spaces are obtained by assuming that the number of cyclic sets is odd. An example is also given to show the validity of our main results.

In this paper, we obtain some new fixed point theorems for (?,?,?,?) -contractive multi-valued mappings in ?-?-T-complete Menger PM-spaces, which turn out to generalize many results in existing literatures. Some examples are also given to illustrate the definition and support our new results. Moreover, some interesting fixed point results endowed with binary relations or graphs are derived as applications of our main results.

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

The aim of this paper is to present the concept of binary comparable operators in partially ordered Banach spaces and prove several fixed point theorems under some contractive conditions. The results of this paper can be used to investigate a large class of nonlinear problems. As an application, we study the existence of solution of a nonlinear integral equation.

In this paper, we study the following quasilinear Schrodinger equations −Δu+V(x)u+κ2Δ(u2)u=f(u)+μ|u|2*−2u, x∈RN, where N ≥ 3, κ > 0, μ ≥ 0, and V:RN→R satisfy suitable assumptions. First, by using a change of variable and some new skills, we obtain the ground states for this problem with subcritical growth via the Pohozaev manifold. Second, we establish the existence of ground state solutions with critical growth via L∞estimates, which use the method developed by Brezis and Nirenberg [Commun. Pure Appl. Math. 36, 437–477 (1983)] and Jeanjean [Proc. R. Soc. Edinburgh, Sect A. 129, 787–809 (1999)]. Moreover, we give the nonexistence of positive solutions for this problem, where the nonlinear term allow general asymptotically linear growth. Our results extend and supplement the results obtained by Severo et al. [J. Differ. Equations 263, 3550–3580 (2017)], Xu and Chen [J. Differ. Equations 265, 4417–4441 (2018)], and Lehrer and Maia [J. Funct. Anal. 266, 213–246 (2014)] and some other related literature.In this paper, we study the following quasilinear Schrodinger equations −Δu+V(x)u+κ2Δ(u2)u=f(u)+μ|u|2*−2u, x∈RN, where N ≥ 3, κ > 0, μ ≥ 0, and V:RN→R satisfy suitable assumptions. First, by using a change of variable and some new skills, we obtain the ground states for this problem with subcritical growth via the Pohozaev manifold. Second, we establish the existence of ground state solutions with critical growth via L∞estimates, which use the method developed by Brezis and Nirenberg [Commun. Pure Appl. Math. 36, 437–477 (1983)] and Jeanjean [Proc. R. Soc. Edinburgh, Sect A. 129, 787–809 (1999)]. Moreover, we give the nonexistence of positive solutions for this problem, where the nonlinear term allow general asymptotically linear growth. Our results extend and supplement the results obtained by Severo et al. [J. Differ. Equations 263, 3550–3580 (2017)], Xu and Chen [J. Differ. Equations 265, 4417–4441 (2018)], and Lehrer and Maia [J. Funct. Anal. 266, 213–246 (2014)] and some other related literature.

In this paper, we introduce the concept of partial cone b-metric spaces as a generalization of partial metric, cone metric and b-metric spaces and establish some topological properties of partial cone b-metric spaces. Moreover, we also prove some common fixed point theorems for cyclic contractive mappings in such spaces. Our results generalize and extend the main results of Huang and Zhang [Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332:1468–1476, 2007], Stanic et al. [Common fixed point under contractive condition of Ciric's type on cone metric type spaces, Fixed Point Theory Appl., 2012:35, 2012] and Latif et al. [Fixed point results for generalized (α,ψ)‐Meir–Keeler contractive mappings and applications, J. Inequal. Appl., 2014:68, 2014]. Some examples and an application are given to support the usability of the obtained results.

In this work, we introduce a new φ-contractive mapping; following that, we obtain some multipled common fixed point theorems for a pair of mappings $T: \underbrace{X \times X \times\cdots\times X}_{m\text{-times}}\rightarrow X$ and $A: X\rightarrow X$ . The main results of this paper are generalization of the main results of Kutbi et al. (Fixed Point Theory Appl. 2015(1):32, 2015). As an illustration, we give an example to demonstrate the validity of the obtained results.

In this paper, we investigate some nonlinear operator problems and the theory of topological degree. Meanwhile, we obtain some new fixed point theorems in the M-PN space.

In this paper, we first introduce the concepts of generalized ( ψ , f ) λ -expansive mappings and generalized ( ϕ , g , h ) λ -weakly expansive mappings designed for three mappings. Then we establish some common fixed point results for such two new types of mappings in partial b-metric spaces. These results generalize and extend the main results of Karapınar et al. (J. Inequal. Appl. 2014:22, 2014), Nashine et al. (Fixed Point Theory Appl. 2013:203, 2013) and many comparable results from the current literature. Moreover, some examples and an application to a system of integral equations are given here to illustrate the usability of the obtained results. MSC:47H10, 54H25.

Some common fixed point theorems for a family of non-self mappings defined on a closed subset of a metrically convex cone metric space (over the cone which is not necessarily normal) are obtained which generalize earlier results due to Imdad et al. and Janković et al. MSC:47H10, 54H25.

We extend a common fixed point theorem of Radenovic and Rhoades for four non-self-mappings in cone metric spaces.

Some new bounded conditions are constructed in Menger PN spaces,meanwhile,solutions of some nonlinear operator equations are obtained by virtue of topological degree.The main results obtained in this paper improve the recent ones.Furthermore,the new conclusions are applied to a special equation.

In this paper, we obtain some Suzuki-type fixed point theorems for generalized mappings in partial cone metric spaces over a solid cone. Our results unify and generalize various known comparable results in the literature. We also provide illustrative examples in support of our new results.