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The paper deals with the achievement of introducing the notion of F-cone metric spaces over Banach algebra as a generalization of $N_{p}$ -cone metric space over Banach algebra and $N_{b}$ -cone metric space over Banach algebra and studying some of its topological properties. Also, here we define generalized Lipschitz and expansive maps for such spaces. Moreover, we investigate some fixed points for mappings satisfying such conditions in the new framework. Subsequently, as an application of our results, we provide an example. Our results generalize some well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a formula for the M-constants $\mu_{n}(l_{\Phi,p})$ of Orlicz sequence spaces $l_{\Phi,p}$ equipped with the p-Amemiya norm as well as for the equalities $\mu_{n}(l_{\Phi,p})=n$ for any $n\in \mathcal{N}$ are given. Moreover, the Fatou property, weak orthogonality, and the weak fixed point property of these spaces are discussed. Finally a direct formula for the Dominguez-Benavides coefficient of the spaces $l_{\Phi,p}$ is given in terms of the Orlicz function generating these spaces. Both, M-constants and Dominguez-Benavides coefficient, are strongly related to the fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of a cyclic generalized proximal contraction, and then prove some best proximity point theorems in metric spaces. We will provide examples to illustrate our results. [ABSTRACT FROM AUTHOR]

Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and convex subset of X and $T: C \rightarrow C$ be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly convex in every direction or a uniformly convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and Göhde's fixed point theorem for monotone nonexpansive mappings. [ABSTRACT FROM AUTHOR]

In this work, we discuss the concept of Banach operator pairs in modular vector spaces. We prove the existence of common fixed points for these type of operators which satisfy a modular continuity in modular compact sets. On the basis of our result, we are able to give an analog of DeMarr's common fixed point theorem for a family of symmetric Banach operator pairs in modular vector spaces. [ABSTRACT FROM AUTHOR]

In this paper we introduce a family of weakly contractive maps on the space $B(S)$ of bounded real valued functions and use it to show that a fundamental step in the proof of the well-known Stone-Weierstrass approximation theorem can be achieved via Rakotch's fixed point theorem for weakly contractive maps. With the same technique, we obtain Zemanek's theorem on the existence of square roots in certain Banach subalgebras of $B(S)$, and, finally, in the context of abstract Banach algebras, we exhibit some relationship between weakly contractive maps on the closed unit ball and the geometry of the spheres. [ABSTRACT FROM AUTHOR]

In this work, we define the concept of G-monotone nonexpansive multivalued mappings defined on a metric space with a graph G. Then we obtain sufficient conditions for the existence of fixed points for such mappings in hyperbolic metric spaces. This is the first kind of such results in this direction. [ABSTRACT FROM AUTHOR]

Let $(X,\|\cdot\|)$ be a Banach space. Let C be a nonempty, bounded, closed, and convex subset of X and $T: C \rightarrow C$ be a monotone nonexpansive mapping. In this paper, it is shown that a technique of Mann which is defined by is fruitful in finding a fixed point of monotone nonexpansive mappings. [ABSTRACT FROM AUTHOR]

Let $\rho\in\Re$ (the class of all nonzero regular function modulars defined on a nonempty set Ω) and G be a directed graph defined on a subset C of $L_{\rho}$. In this paper, we discuss the existence of fixed points of monotone G-contraction and G-nonexpansive mappings in modular function spaces. These results are the modular version of Jachymski fixed point results for mappings defined in a metric space endowed with a graph. [ABSTRACT FROM AUTHOR]

A new class of multivalued non-self-mappings, called SK-contractions with respect to b-generalized pseudodistances, is introduced and used to investigate the existence of best proximity points by using an appropriate geometric property. Some new fixed point results in b-metric spaces are also obtained. Examples are given to support the usability of our main results. [ABSTRACT FROM AUTHOR]

We introduce a new geometric constant $C_{NJ}^{(p)}(X)$ for a Banach space X, called a generalized von Neumann-Jordan constant. Next, it is shown that $1\leq C_{NJ}^{(p)}(X)\leq2$ for any Banach space X and that the right hand side inequality is sharp if and only if X is uniformly non-square. Moreover, a relationship between the James constant $J(X)$ and $C_{NJ}^{(p)}(X)$ is presented. Finally, the generalized von Neumann-Jordan constant of the Lebesgue space $L_{r}([0,1])$ is calculated and a relationship between $C_{NJ}^{(p)}(X)$ and the fixed point property is found. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the common fixed points set of nonexpansive semigroups of nonlinear mappings $\{T_{t}\}_{t \geq0}$, i.e., a family such that $T_{0}(x)=x$, $T_{s+t}=T_{s}(T_{t}(x))$, where the domain is a metric space $(M,d)$. In particular we prove that under suitable conditions, the common fixed points set is the same as the common fixed points set of two mappings from the family. Then we use the modified Mann iteration process to approximate such common fixed points. [ABSTRACT FROM AUTHOR]

In this work, we define the concept of G-monotone nonexpansive multivalued mappings defined on a metric space with a graph G. Then we obtain sufficient conditions for the existence of fixed points for such mappings in hyperbolic metric spaces. This is the first kind of such results in this direction. [ABSTRACT FROM AUTHOR]

We give a generalization of the Banach contraction principle on a modular metric space endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as the modular metric version of Jachymski's fixed point result for mappings on a metric space with a graph. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of fixed points of monotone nonexpansive mappings defined in Banach spaces endowed with a graph. This work is a continuity of the previous results of Ran and Reurings, Nieto et al., and Jachimsky done for contraction mappings defined in metric spaces endowed with a graph. [ABSTRACT FROM AUTHOR]

In this paper, we investigate common solutions to a family of mixed equilibrium problems with a relaxed η- α-monotone mapping and a nonlinear operator equation involving an infinite family of asymptotically quasi- ϕ-nonexpansive mappings in the intermediate sense. Strong convergence theorems of common solutions are established in a strictly convex and uniformly smooth Banach space. These results extend many important recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the common approximate fixed points of monotone nonexpansive semigroups of nonlinear mappings $\{T(t)\}_{t \geq0}$, i.e., a family such that $T(0)x=x$, $T(s+t)x=T(s)\circ T(t)x $, where the domain is a Banach space. In particular we prove that under suitable conditions, the common approximate fixed points are the same as the common approximate fixed points set of two mappings from the family. Then we give an algorithm of how to construct an approximate fixed point sequence of the semigroup in the case of a uniformly convex Banach space. [ABSTRACT FROM AUTHOR]

In this work, we discuss the existence of fixed points of monotone nonexpansive mappings defined on partially ordered Banach spaces. This work is a continuity of the previous works of Ran and Reurings, Nieto et al., and Jachimsky done for contraction mappings. As an application, we discuss the existence of solutions to an integral equations. [ABSTRACT FROM AUTHOR]

In this work, we introduce the $(\mathit{CLR})$-property for the hybrid pairs of single-valued and multi-valued mappings and give some coincidence and common fixed point theorems for the hybrid pairs of some contractive conditions. Also, we will give some examples to illustrate the main results in this paper. Our results extend and improve some results given by some authors. [ABSTRACT FROM AUTHOR]

In this work we define the new concept of monotone pointwise contraction mappings in Banach and metric spaces. Then we prove the existence of fixed points of such mappings. [ABSTRACT FROM AUTHOR]

In this work, we give a new definition of G-monotone pointwise contraction mappings in metric spaces endowed with a graph. Then we obtain sufficient conditions for the existence of a fixed point for such mappings. The proofs are based on the crucial inequality (GK). [ABSTRACT FROM AUTHOR]

Let the set $C \subset L_{1}([0,1])$ be nonempty, convex and compact for the convergence almost everywhere and $T: C \rightarrow C$ be a monotone nonexpansive mapping. In this paper, we study the behavior of the Krasnoselskii-Ishikawa iteration sequence $\{f_{n}\}$ defined by $f_{n+1} = \lambda f_{n} + (1-\lambda)T(f_{n})$, $n = 1, 2, \ldots$ , $\lambda\in(0,1)$. Then we prove a fixed point theorem for these mappings. Our result is new and was never investigated. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the common fixed points set of nonexpansive semigroups of nonlinear mappings $\{T_{t}\}_{t \geq0}$, i.e., a family such that $T_{0}(x)=x$, $T_{s+t}=T_{s}(T_{t}(x))$, where the domain is a metric space $(M,d)$. In particular we prove that under suitable conditions, the common fixed points set is the same as the common fixed points set of two mappings from the family. Then we use the modified Mann iteration process to approximate such common fixed points. [ABSTRACT FROM AUTHOR]

Let $\rho\in\Re$ (the class of all nonzero regular function modulars defined on a nonempty set Ω) and G be a directed graph defined on a subset C of $L_{\rho}$. In this paper, we discuss the existence of fixed points of monotone G-contraction and G-nonexpansive mappings in modular function spaces. These results are the modular version of Jachymski fixed point results for mappings defined in a metric space endowed with a graph. [ABSTRACT FROM AUTHOR]