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In this work, we establish the closedness and convexity of the set of fixed points of equally continuous and asymptotically demicontractive mapping in the intermediate sense. We proposed an inertial hybrid projection technique for determining an approximate common solution to three significant problems. The first is the system of generalized mixed equilibrium problems with relaxed η−ζ$$ \eta -\zeta $$ monotone mappings, the second is the problem of fixed points of a countable family of equally continuous and asymptotically demicontractive mappings in the intermediate sense, and the third is of determining a point in a null space of a countable family of inverse strongly monotone mappings in Hilbert space. Based on these problems, we formulate a theorem and establish its strong convergence to their common solution. Additionally, we studied the applications of our algorithm to variational inequality problems and convex optimization problems. Finally, we numerically demonstrate the efficiency and robustness of our scheme. Several results available in the literature can be obtained as special cases of our result. [ABSTRACT FROM AUTHOR]

In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappings in this setting. By using an appropriate geodesic averaged perturbation technique, we obtained strong convergence and Δ-convergence theorems for a Krasnoselskij-Mann type iterative algorithm to approximate the fixed points of quasinonexpansive mappings within the framework of CAT(0) spaces. The main results obtained in this nonlinear setting are natural extensions of the classical results from linear settings (Hilbert and Banach spaces) for both quasi-nonexpansive mappings and demicontractive mappings. We applied our results to solving an equilibrium problem in CAT(0) spaces and showed how we can approximate the equilibrium points by using our fixed point results. In this context we also provided a numerical example in the case of a demicontractive mapping that is not a quasi-nonexpansive mapping and highlighted the convergence pattern of the algorithm in Table 1. It is important to note that the numerical example is set in non-Hilbert CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of multivalued demicontractive mappings. We also provide numerical results concerning the viability of the proposed algorithm with possible applications. [ABSTRACT FROM AUTHOR]

This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for ρ$$ \rho $$‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable step size rules that do not require prior knowledge of the operator value. Our algorithms employ a basic step size rule, which is derived by certain computations at each iteration. Without previous knowledge of the operators Lipschitz constant, two strong convergence theorems were obtained. Finally, we present a number of numerical experiments to evaluate the efficacy and applicability of the proposed algorithms. The conclusions of this study on variational inequality and fixed point problems support and extend previous findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce graphic contraction mappings in b-metric spaces and establish some fixed point theorems in the aforesaid space. Appropriate graphs are presented to visualize related definitions and concepts. On the other hand, some examples are presented to verify the authenticity and effectiveness of the established results. Our results generalize and extend some pioneer results existing in the literature. Moreover, applications to existence of solution for ordinary differential equations and for integral equations are also established to show the adequacy of our results. [ABSTRACT FROM AUTHOR]

Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1-14], we introduce a new class of G-f-contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph. [ABSTRACT FROM AUTHOR]

In this paper, we prove some random fixed point theorems for Hardy-Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach spaces. Some stochastic versions of deterministic fixed point theorems for Hardy-Rogers self mappings and stochastic integral equations are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point results for fuzzy mappings in a complete dislocated b-metric space. Our results generalize and extend the results of Joseph et al. (SpringerPlus 5:Article ID 217, 2016). We also give examples to support our results, and applications relating the results to a fixed point for multivalued mappings and fuzzy mappings are studied. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and prove some classes of fuzzy contractive mappings with altering distance function via α and βκ-admissible mappings in the fuzzy metric spaces. We also give some example and graph which demonstrate the validity of the hypotheses of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature. As an application to our main result a fixed point for contraction mappings of integral type in fuzzy metric spaces are presented. [ABSTRACT FROM AUTHOR]

In paper, we prove some common fixed point theorems for the pair of self-mappings with the g-quasi-condition in modular metric spaces. Also, we modify and prove some common fixed point theorems by using the (CLRg)-property along with the weakly compatible mapping. Finally, we give some applications on integral equations to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove some strong and Δ-convergence theorems of the modified S-iteration for (α, β)-generalized hybrid mappings in CAT(0) spaces. Our results improve and extend the corresponding recent results announced in [1] and some papers. [ABSTRACT FROM AUTHOR]

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. In this paper we investigate some fixed-point theorems in modular metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a general Bayesian abstract fuzzy economy model of product measurable spaces, and we prove the existence of Bayesian fuzzy equilibrium for this model. Our results extend and improve the corresponding recent results announced by Patriche and many authors from the literature. It captures the idea that the uncertainties characterize the individual feature of the decisions of the agents involved in different economic activities. In this paper, the uncertainties can be described by using random fuzzy mappings. Further attention is needed for the study of applications of the established result in the game theory and the fuzzy economic field.Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The aim of this work is to establish some new fixed point theorems for generalized F-Suzuki-contraction mappings in complete b-metric spaces. [ABSTRACT FROM AUTHOR]

In this manuscript, common fixed point results for self-mappings satisfying generalized weak integral type contraction in the setting of G-metric space are established. Using the derived results, some applications to the systems of non-linear integral and fractional differential equations are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we state and prove Wardowski type fixed point theorems in metric space by using a modified generalized F-contraction maps. These theorems extend other well-known fundamental metrical fixed point theorems in the literature (Dung and Hang in Vietnam J. Math. 43:743-753, and Piri and Kumam in Fixed Point Theory Appl. 2014:210, , etc.). Examples are provided to support the usability of our results. [ABSTRACT FROM AUTHOR]

We introduce the notion of a modified α- ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory. [ABSTRACT FROM AUTHOR]

In this paper, we prove common coupled fixed point theorems under a Geraghty-type condition using monotone instead of the often used mixed monotone property. Also we give some sufficient conditions for the uniqueness of a common coupled fixed point. An example illustrating our results is provided. [ABSTRACT FROM AUTHOR]

The object of this paper is to extend the concept of β-admissible for multivalued mappings due to Mohammadi et al. [B. Mohammadi, S. Rezapour and N. Shahzad, Some results on fixed points of α-ψ-Ciric generalized multifunctions, Fixed Point Theory and Applications 2013 (2013), 24] to fuzzy mappings and utilize this concept to prove a common α-fuzzy fixed point theorem for a pair of fuzzy mappings. We also give illustrative example which demonstrate the validity of the hypotheses of our results. Some related results to common fixed point for multivalued mappings are also derived from the main result. [ABSTRACT FROM AUTHOR]

In this paper, we extend the concept of contraction mappings in b-metric spaces and utilize this concept to prove the existence and uniqueness of fixed point theorems for such mappings in such a space. We also prove the generalized Ulam-Hyers stability and well-posed results for a fixed point equation employing the concept of α-admissibility in b-metric spaces. We shall construct some examples to support our novel results. [ABSTRACT FROM AUTHOR]

In this paper we consider some new definitions about quadrupled fixed point in abstract metric spaces and obtain some new fixed point results in this field. These results unify, extend and generalize well-known comparable results in the existing literature. We also provide some examples and applications to support our results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce viscosity approximation methods based on generalized contraction mappings for finding a set of common fixed points of a countable family of strict pseudo-contraction mappings, the common element of the set solutions of a general system of variational inequalities with Lipschitzian and relaxed cocoercive mappings and the set of solutions of a generalized mixed equilibrium problem. Furthermore, strong convergence theorems of the purposed iterative process are established in the framework of Banach spaces. The results presented in this paper improve and extend many recent important results. [Copyright &y& Elsevier]

In this paper, we introduce a new hybrid iterative scheme for finding a common element of the set of zeroes of a maximal monotone operator, the set of fixed points of a relatively quasi-nonexpansive mapping, the sets of solutions of an equilibrium problem and the variational inequality problem in Banach spaces. As applications, we apply our results to obtain strong convergence theorems for a maximal monotone operator and quasi-nonexpansive mappings in Hilbert spaces and we consider a problem of finding a minimizer of a convex function. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce the new notion which is more general than the previous works on the weakly isotone mappings in the case of single valued mappings and multivalued mappings in an ordered Banach space. We also extend some common fixed point theorems of Dhage et al. [4] and give some applications of the main results. Furthermore, at the end of this paper, we give an open problem for further investigation. [Copyright &y& Elsevier]

In this paper, we introduce and consider a new generalized system of nonlinear mixed variational inequality involving three difference relaxed cocoercive operators. This work is to use the resolvent operator technique to find the common solutions for a new generalized system of relaxed cocoercive mixed variational inequality problems and fixed point problems for Lipschitz mappings in Hilbert spaces. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

Recently, Samet et al. (2012) introduced the notion of α-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weak α-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al. [ABSTRACT FROM AUTHOR]

Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which aremore general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate ourmain results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multi-valued mappings. [Copyright &y& Elsevier]

In this paper, we prove a strong convergence theorem for finding a common solutions of a general system of variational inequalities involving two different inverse-strongly accretive operators and solutions of fixed point problems involving the nonexpansive mapping in a Banach space by using a modified viscosity extragradient method with weak contraction. Moreover, using the above results, we can apply to finding solutions of zeros of accretive operators and the class of k-strictly pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of Qin et al. [Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications, J. Comput. Appl. Math., 233 (2009), 231-240.], Aoyama et al. [Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory and Applications, vol. 2006, Article ID 35390, 1-13.], Yao et al. [Modified extragradient methods for a system of variational inequalities in Banach spaces, Acta. Appl. Math., 110(3) (2010), 1211-1224.], Katchang et al. [A viscosity iterative scheme for inverse-strongly accretive operators in Banach spaces, Journal of Computational Analysis and Applications, 12(3) (2010), 678 686.] and many others. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding the common solution of a system of mixed equilibrium problems of bifunctions satisfying certain the conditions and the common solution of variational inequality problems of inverse strongly monotone mappings and the common solution of fixed point problems for a family of uniformly Lipschitzian continuous and asymptotically -strict pseudocontractive mapping in the intermediate sense. We prove the strong convergence theorem for a new iterative algorithm under some mild conditions in Hilbert spaces. Finally, we also give some numerical examples for support our results. [Copyright &y& Elsevier]

In this paper, we introduce and study the random nonlinear variational inclusion problem with multi-valued random operators. We define a random iterative algorithm for finding the approximate solutions of class of random variational inclusions and establish the convergence of random iterative sequence generated by proposed algorithm in a uniformly smooth Banach space. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce the notion of a hybrid generalized multi-valued contraction mapping and establish the common fixed point theorem for this mapping. Our results generalize, unify, extend and complement several common fixed point theorems of many authors in the literature. [Copyright &y& Elsevier]

The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-f-nonexpansive mappings in Banach spaces. Moreover, the strong convergence theorems of this method are established under the suitable conditions of the parameter imposed on the algorithm. Finally, we apply our results to finding a zero point of inverse-strongly monotone operators and complementarity problems. Our results presented in this paper improve and extend the recently results by many others. [ABSTRACT FROM AUTHOR]

We generalized the notion of proximal contractions of the first and the second kinds and established the best proximity point theorems for these classes. Our results improve and extend recent result of Sadiq Basha (2011) and some authors. [ABSTRACT FROM AUTHOR]

We introduce an implicit-relation-type cyclic contractive condition for a map in a metric space and derive existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the paper, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented. [ABSTRACT FROM AUTHOR]

We extend the recent results of the coupled fixed point theorems of Cho et al. (2012) by weakening the concept of the mixed monotone property. We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. The main results extend and unify the results of Cho et al. and many results of the coupled fixed point theorems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part. [ABSTRACT FROM AUTHOR]

In this article, we define a tangential property which can be used not only for single-valued mappings but also for multi-valued mappings, and used it in the prove for the existence of a common fixed point theorems of Gregus type for four mappings satisfying a strict general contractive condition of integral type in metric spaces. Our theorems generalize and unify main results of Pathak and Shahzad (Bull. Belg. Math. Soc. Simon Stevin 16, 277-288, 2009) and several known fixed point results. [ABSTRACT FROM AUTHOR]

Abstract: Kirk and Xu introduced the concept of asymptotic pointwise contractions. In this paper, we investigate these kinds of mappings in modular spaces. Moreover, the fixed point theorem for asymptotic pointwise nonexpansive mappings in modular spaces is also studied. The results of this paper improve and extend the results of Razani et al. [A. Razani, E. Nabizadeh, M. Beyg Mohamadi, S. Homaei Pour, Fixed points of nonlinear and asymptotic contractions in the modular spaces, Abstract and Applied Analysis, 2007 (2007)], and Kirk and Xu [W. A. Kirk, Hong-Kun Xu, Asymptotic pointwise contractions, Nonlinear Analysis 69 (2008) 4706–4712] to modular spaces. [Copyright &y& Elsevier]

In this paper, we introduce an iterative scheme based on a viscosity approximation method with a modified extragradient method for finding a common solutions of a general system of variational inequalities for two inverse-strongly accretive operator and solutions of fixed point problems involving the nonexpansive mapping in Banach spaces. Consequently, we obtain new strong convergence theorems in the frame work of Banach spaces. Our results extend and improve the recent results of Qin et al. (J Comput Appl Math 233:231-240, 2009) and many others. [ABSTRACT FROM AUTHOR]

Abstract: In 2007, Kamran [T. Kamran, Multivalued -weakly Picard mappings, Nonlinear Anal. 67 (2007) 2289–2296] extended the notion of multi-valued mapping from weak contraction and generalized -weak contraction to -weak contraction and generalized multi-valued -weak contraction. He also obtained some common fixed point theorems with the notion of -weakly commuting at a coincidence point of a hybrid pair. In this paper, we can drop the condition of -weakly commuting in Theorems 2.9 and 3.5 in . We further extend the notion of generalized multi-valued -weak contraction and introduce the notion of generalized multi-valued -weak contraction. We also establish some coincidence and common fixed point theorems with generalized multi-valued -weak contraction mappings. Our results extend and generalize several common fixed point theorems of many authors. [Copyright &y& Elsevier]

We introduce an iterative algorithm for finding a common element of the set of fixed points of strict pseudocontractions mapping, the set of common solutions of a system of two mixed equilibrium problems and the set of common solutions of the variational inequalities with inverse strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. Finally, we apply our results for solving convex feasibility problems in Hilbert spaces. Our results improve and extend the corresponding results announced by many others recently. [ABSTRACT FROM AUTHOR]

We prove new fixed point and common fixed point theorems for generalized weak contractive mappings of integral type in modular spaces. Our results extend and generalize the results of A. Razani and R. Moradi (2009) and M. Beygmohammadi and A. Razani (2010). [ABSTRACT FROM AUTHOR]

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu (2006), Su et al. (2008), Klin-eam and Suantai (2009), Tan and Chang (2011), and some other authors. [ABSTRACT FROM AUTHOR]

We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others. [ABSTRACT FROM AUTHOR]

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was obtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu (2011), Zhang et al. (2008), and many authors. [ABSTRACT FROM AUTHOR]