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In this paper, we provide a new approach for discussing the solvability of a class of operator equations by establishing fixed point theorems in locally convex spaces. Our results are obtained extend some Krasnosel'skii type fixed point theorems. As an application, we investigate the existence and global attractivity of solutions for a general nonlinear integral equation of mixed type of Urysohn and Volterra. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new idea to investigate the important basic problem: how to extend Darbo' s fixed point theorem? We establish some new generalizations of Darbo's fixed point theorem by using 'integral conditions'. Our fixed point theorems extend the existing results on the problem above. [ABSTRACT FROM AUTHOR]

The first purpose of this paper is to define a homotopy for fuzzy spaces. We continue our work by showing that the property of having a fixed point is invariant by this homotopy. These theorems generalize and improve well-known results. [ABSTRACT FROM AUTHOR]

In this paper, we establish several fixed point theorems for Meir-Keeler type contractions in partially ordered G-metric spaces. [ABSTRACT FROM AUTHOR]

Meir and Keeler formulated their fixed point theorem for contractive mappings with purely metric condition. This idea was extended by numerous mathematicians. In this paper, we present a simple method of proving such theorems and give new results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of fixed points for nonlinear and semilinear operators on order intervals. The abstract results unified some methods in studying the existence of positive solutions for boundary and initial value problems of nonlinear difference and differential equations. Applications are shown by examples. [ABSTRACT FROM AUTHOR]

In this paper, we prove sharpened versions of some classical order-theoretic metrical fixed point theorems due to Nieto and Rodríguez-López (Order 22(3):223-239, 2005) using order-theoretic variants of completeness and continuity besides some another notions such as: the ICC property, the DCC property, and the MCC property. In this continuation, we further extend our results for Boyd-Wong type nonlinear contractions. Finally, as an application of our certain newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem. [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]

In this paper, we present a new proof of the Mazur-Orlicz theorem, which uses the Markov-Kakutani common fixed point theorem, and a new proof of the Markov-Kakutani common fixed point theorem, which uses the Mazur-Orlicz theorem. [ABSTRACT FROM AUTHOR]

In this paper, several kinds of generalized vector quasi-equilibrium problems are introduced and studied in abstract convex spaces. Using the properties of Γ-convex and $\mathfrak{KC}$-maps, some sufficient conditions are given to guarantee the existence of solutions in connection with these generalized vector quasi-equilibrium problems. As applications, some existence theorems of solutions for the generalized semi-infinite programs with vector quasi-equilibrium constraints are also given. [ABSTRACT FROM AUTHOR]

In the paper, we introduce a new hybrid algorithm which is not based on the modification to weak convergence algorithms. The strong convergence theorem of the proposed algorithm is presented. Finally, the numerical experiments suggest that the new algorithm could be faster than Nakajo and Takahashi's algorithm in J. Math. Anal. Appl. 279:372-379, 2003. [ABSTRACT FROM AUTHOR]

In this paper, a new modified Ishikawa iterative algorithm with errors by a shrinking projection method for generalized mixed equilibrium problems and a countable family of uniformly Bregman totally quasi- D-asymptotically nonexpansive mappings is introduced and investigated in the framework of a real Banach space. Strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results in this field. [ABSTRACT FROM AUTHOR]

In this paper, we prove some strong and △-convergence theorems for a finite family of multivalued quasi-nonexpansive mappings satisfying condition $(E)$ in $\operatorname{CAT}(\kappa)$ spaces. Our results extend the corresponding results of Abkar and Eslamian (Nonlinear Anal. 75:1895-1903, 2012), Panyanak (Fixed Point Theory Appl. 2014:1, 2014), Shahzad and Zegeye (Nonlinear Anal. 71:838-844, 2009) and many others. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to obtain some new common fixed point theorems for Geraghty's type contraction mappings using the monotone property with two metrics and to give some examples to illustrate the main results. Further, by using our main results, we prove some results about multidimensional common fixed points. Our results generalize and extend some recent results given by Kadelburg et al. (Fixed Point Theory Appl. 2015:27, 2015) and Choudhurya and Kundu (J. Nonlinear Sci. Appl. 5:259-270, 2012). [ABSTRACT FROM AUTHOR]

Very recently, the notion of a Ψ-Geraghty type contraction was defined by Gordji et al. (Fixed Point Theory and Applications 2012:74, 2012). In this short note, we realize that the main result via Ψ-Geraghty type contraction is equivalent to an existing related result in the literature. Consequently, all results inspired by the paper of Gordji et al. in (Fixed Point Theory and Applications 2012:74, 2012) can be derived in the same way. [ABSTRACT FROM AUTHOR]

By using the projection methods, we suggest and analyze the iterative schemes for finding the approximation solvability of a system of general variational inequalities involving different nonlinear operators in the framework of Hilbert spaces. Moreover, such solutions are also fixed points of a Lipschitz mapping. Some interesting cases and examples of applying the main results are discussed and showed. The results presented in this paper are more general and include many previously known results as special cases. [ABSTRACT FROM AUTHOR]

We consider a new iterative algorithm for finding a common element of the set of generalized mixed equilibrium problems, the set of solutions of a system of quasivariational inclusions for two difference inverse strongly accretive operators, and common set of fixed points for strict pseudocontraction mappings in Banach spaces. Furthermore, strong convergence theorems of this method were established under suitable assumptions imposed on the algorithm parameters. The results obtained in this paper improve and extend some results in the literature. [ABSTRACT FROM AUTHOR]

In this paper at first we introduce a new order on the subsets of cone metric spaces then, using this definition, we simplify the proof of fixed point theorems for contractive set-valued maps, omit the assumption of normality, and obtain some generalization of results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the problem of approximating a common element of the set of fixed points of a demicontractive mapping and the set of solutions of a mixed equilibrium problem. First, we propose an extragradient method for solving the mixed equilibrium problems and the fixed point problems. Subsequently, we prove the strong convergence of the proposed algorithm under some mild assumptions. [ABSTRACT FROM AUTHOR]

A lot of authors have proved various common fixed-point results for pairs of self-mappings under strict contractive conditions in metric spaces. In the case of cone metric spaces, fixed point results are usually proved under assumption that the cone is normal. In the present paper we prove common fixed point results under strict contractive conditions in cone metric spaces using only the assumption that the cone interior is nonempty. We modify the definition of property (E.A), introduced recently in the work by Aamri and Moutawakil (2002), and use it instead of usual assumptions about commutativity or compatibility of the given pair. Examples show that the obtained results are proper extensions of the existing ones. [ABSTRACT FROM AUTHOR]

The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive mapping, but it cannot be used for hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi (2005), and some others. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present existence, uniqueness, and data dependence results for the strict fixed points of a multivalued operator of Reich type, as well as, some sufficient conditions for the well-posedness of a fixed point problem for the multivalued operator. [ABSTRACT FROM AUTHOR]

Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space E∗. In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational inequality problems and fixed points of a countable family of relatively nonexpansive maps. The theorems proved are improvement of the results of Censor et al. (J. Optim. Theory Appl. 148:318-335, 2011). [ABSTRACT FROM AUTHOR]

The Schauder fixed point theorem is extended to the context of metric spaces with global nonpositive curvature. Some applications are included. [ABSTRACT FROM AUTHOR]

By applying the fixed point method, we will prove the Hyers-Ulam-Rassias stability of the functional equation f(x + y) = F[f(x), f(y)] under some additional assumptions on the function F and spaces involved. [ABSTRACT FROM AUTHOR]

Several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps satisfying generalized contractive conditions are established in a symmetric space. [ABSTRACT FROM AUTHOR]

In this manuscript we extend very recent fixed point theorems in the setting of Menger spaces in three senses: on the one hand, we introduce the notion of Menger probabilistic metric-like space by avoiding a non-necessary constraint (at least, for our purposes) in the properties that define a Menger space; on the other hand, we consider a more general class of auxiliary functions in the contractivity condition; finally, we show that the function $t\rightarrow1/t-1$ (which appears in many fixed point theorems in the fuzzy context) can be replaced by more appropriate and general functions. We illustrate our main statements with an example in which previous results cannot be applied. [ABSTRACT FROM AUTHOR]

A proximal point algorithm with double computational errors for treating zero points of accretive operators is investigated. Strong convergence theorems of zero points are established in a Banach space. [ABSTRACT FROM AUTHOR]

We generalize and modify Lefschetz sets defined in 1976 by L. Górniewicz, which leads to more general results in fixed point theory. [ABSTRACT FROM AUTHOR]

We use the order relation on uniform spaces defined by Altun and Imdad (2009) to prove some new fixed-point and coupled fixed-point theorems for multivaluedmonotone mappings in ordered uniform spaces. [ABSTRACT FROM AUTHOR]

We consider the equivalence of the existence of fixed points of single-valued mappings and multivalued mappings for some classes of mappings by proving some equivalence theorems for the completeness of metric spaces. [ABSTRACT FROM AUTHOR]

We prove some fixed point results for mappings satisfying various contractive conditions on Complete G-metric Spaces. Also the Uniqueness of such fixed point are proved, as well as we showed these mappings are G-continuous on such fixed points. [ABSTRACT FROM AUTHOR]

Robust stability results for nominally linear hybrid systems are obtained from total stability theorems for purely continuous-time and discrete-time systems by using the powerful tool of fixed point theory. The class of hybrid systems dealt consists, in general, of coupled continuous-time and digital systems subject to state perturbations whose nominal (i.e., unperturbed) parts are linear and, in general, time-varying. The obtained sufficient conditions on robust stability under a wide class of harmless perturbations are dependent on the values of the parameters defining the overbounding functions of those perturbations. The weakness of the coupling dynamics in terms of norm among the analog and digital substates of the whole dynamic system guarantees the total stability provided that the corresponding uncoupled nominal subsystems are both exponentially stable. Fixed point stability theory is used for the proofs of stability. A generalization of that result is given for the case that sampling is not uniform. The boundedness of the state-trajectory solution at sampling instants guarantees the global boundedness of the solutions for all time. The existence of a fixed point for the sampled state-trajectory solution at sampling instants guarantees the existence of a fixed point of an extended auxiliary discrete system and the existence of a global asymptotic attractor of the solutions which is either a fixed point or a limit n globally stable asymptotic oscillation. [ABSTRACT FROM AUTHOR]

In recent literature concerning fixed point theory for self-mappings T : X → X in metric spaces (X, d), there are some new concepts which can be mutually related so that the inherent properties of each one might be combined for such self-mappings. Self-mappings T : X → X can be referred to, for instance, as Kannan-mappings, reasonable expansive mappings, and Picard T-stable mappings. Some relations between such concepts subject either to sufficient, necessary, or necessary and sufficient conditions are obtained so that in certain self-mappings can exhibit combined properties being inherent to each of its various characterizations. [ABSTRACT FROM AUTHOR]

Using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms in C*-algebras and Lie C*-algebras and of derivations on C*-algebras and Lie C*-algebras for the Cauchy functional equation. [ABSTRACT FROM AUTHOR]

We establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk (1988). Also, an example is given to support our generalization. We also prove common fixed point theorems for weakly compatible mappings in metric and compact metric spaces. [ABSTRACT FROM AUTHOR]

We use a concept of abstract convexity to define the almost S-KKMc property, al-S-KKMc(X, Y) family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors. [ABSTRACT FROM AUTHOR]

We generalize, extend, and improve some recent fixed point results in cone metric spaces including the results of H. Guang and Z. Xian (2007); P. Vetro (2007); M. Abbas and G. Jungck (2008); Sh. Rezapour and R. Hamlbarani (2008). In all our results, the normality assumption, which is a characteristic of most of the previous results, is dispensed. Consequently, the results generalize several fixed results in metric spaces including the results of G. E. Hardy and T. D. Rogers (1973), R. Kannan (1969), G. Jungck, S. Radenovic, S. Radojevic, and V. Rakocevic (2009), and all the references therein. [ABSTRACT FROM AUTHOR]

We prove several fixed point theorems on cone metric spaces in which the cone does not need to be normal. These theorems generalize the recent results of Huang and Zhang (2007), Abbas and Jungck (2008), and Vetro (2007). Furthermore as corollaries, we obtain recent results of Rezapour and Hamlborani (2008). [ABSTRACT FROM AUTHOR]

We prove a general principle in Random Fixed Point Theory by introducing a condition named (ρ) which was inspired by some of Petryshyn's work, and then we apply our result to prove some random fixed points theorems, including generalizations of some Bharucha-Reid theorems. [ABSTRACT FROM AUTHOR]

We discuss three classes of generalized implicit vector equilibrium problems in topological ordered spaces. Under some conditions, we prove three new existence theorems of solutions for the generalized implicit vector equilibrium problems in topological ordered spaces by using the Fan- Browder fixed point theorem. [ABSTRACT FROM AUTHOR]

We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results. [ABSTRACT FROM AUTHOR]

We consider complete Menger probabilistic quasimetric space and prove common fixed point theorems for weakly compatible maps in this space. [ABSTRACT FROM AUTHOR]

We prove some results on the existence of fixed points for multivalued generalized w-contractive maps not involving the extended Hausdorff metric. Consequently, several known fixed point results are either generalized or improved. [ABSTRACT FROM AUTHOR]

We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Banach space. [ABSTRACT FROM AUTHOR]

We investigate the existence and uniqueness of solutions φ : I → J of the functional equation φ(f(x))= F(φ(x)), x ∈ I, where I, J are closed intervals, and f : I → I, F : J → J are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result. [ABSTRACT FROM AUTHOR]

Common fixed point results for some new classes of nonlinear noncommuting maps on a locally convex space are proved. As applications, related invariant approximation results are obtained. Our work includes improvements and extension of several recent developments of the existing literature on common fixed points. We also provide illustrative examples to demonstrate the generality of our results over the known ones. [ABSTRACT FROM AUTHOR]

In order to observe the condition of Kannan mappings, we prove a generalization of Kannan's fixed point theorem. Our theorem involves constants and we obtain the best constants to ensure a fixed point. [ABSTRACT FROM AUTHOR]

Some generalized Ky Fan minimax inequalities for vector-valued mappings are established by applying the classical Browder fixed point theorem and the Kakutani-Fan-Glicksberg fixed point theorem. [ABSTRACT FROM AUTHOR]