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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]

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 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 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, 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]

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]

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]

The Hardy-Rogers p-proximal cyclic contraction, which includes the cyclic, Kannan, Chatterjea and Reich contractions as sub-classes, is developed in uniform spaces. The existence and uniqueness results of best proximity points for these contractions are proved. The results, which are for non-self maps, apart from the fact that they are new in literature, generalise several other similar results in literature. Examples are given to validate the results obtained. [ABSTRACT FROM AUTHOR]

In this manuscript, we establish a coincidence point and a unique common fixed point theorem for (ψ,φ)-weak cyclic compatible contractions. We also present a fixed point theorem for a class of Λ-weak cyclic compatible contractions via altering distance functions. Our results extend and improve some well-known results in the literature. We provide examples to analyze and illustrate our main results. [ABSTRACT FROM AUTHOR]