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In this paper, by using symmetric first-order divided differences, we introduce a new family of Secant-like iterative methods with quadratic convergence. Afterthought, we analyze its semilocal and local behavior when the nonlinear operator F is not differentiable by imposing appropriate bounding conditions in each case. Theoretical results have also been tested by solving a problem which shows the applicability of our work. [ABSTRACT FROM AUTHOR]

It is well known that many popular variational, quasi-variational, hemivariational inequalities and variational inclusions involving constraints in a Banach space to convert a fixed point problems for finding the solution of such problems. This paper is to infuse a sequence of penalized problems without constraints and we show under the few reasonable assumptions to the Kuratowski upper limit with respect to the weak topology of the sets of solutions to penalized problems is nonempty. As an application, we explore two complicated partial differential systems of elliptic mixed boundary value problem involving a nonlinear nonhomogeneous differential operator with an obstacle effect, and a nonlinear elastic contact problem in mechanics with unilateral constraints. [ABSTRACT FROM AUTHOR]

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan, Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl. 396 (2012), 536-545]. The obtained multiple fixed point theorems extend, generalise and unify many related results in literature. [ABSTRACT FROM AUTHOR]

Let K be a non-empty closed subset of a Banach space X endowed with a graph G. The main result of this paper is a fixed point theorem for nonself Kannan G-contractions T : K → X that satisfy Rothe's boundary condition, i.e., T maps ∂K (the boundary of K) into K. Our new results are extensions of recent fixed point theorems for self mappings on metric spaces endowed with a partial order and also of various fixed point theorems for self and nonself mappings on Banach spaces or convex metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we give examples of cyclic operators defined on various types of sets, in order to illustrate some results in the extremely rich literature following the seminal paper [Kirk,W. A., Srinivasan, P. S. and Veeramani, P., Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), No. 1, 79 - 89]. All examples which are presented enrich the list of cyclic operators and give a subject to future studies of this type of operators. [ABSTRACT FROM AUTHOR]

In this paper, we present the random version of generalized Caristi's fixed point theorem for generalized distance on Polish spaces. Moreover, we prove some Caristi's random fixed point theorems for multi-valued mappings on Polish spaces. Our results in this paper extend and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study a zero point problem of the sum of two accretive operators based on a viscosity forward-backward iterative algorithm with computational errors. Strong convergence results are established in the framework of q-uniformly smooth Banach spaces. We also apply the strong convergence results to solve variational inequality problems, convex minimization problems and fixed point problems. [ABSTRACT FROM AUTHOR]

Most of the studies about hybrid mappings are carried out for single-valued mappings in Hilbert spaces. We define a new class of multivalued mappings in CAT (κ) spaces which contains the multivalued generalization of (α, β) - hybrid mappings defined on Hilbert spaces. In this paper, we prove existence and convergence results for a new class of multivalued hybrid mappings on CAT(κ) spaces which are more general than Hilbert spaces and CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we construct an iterative process involving a hybrid pair of a Bregman strongly nonexpansive single-valued mapping and a finite family of Bregman relative nonexpansive multi-valued mappings and prove strong convergence theorems of the proposed iterative process in reflexive Banach spaces under appropriate conditions. Our main results can be viewed as an improvement and extension of the several results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, some existence results for a system of operator inclusions are presented. Qualitative properties of the solution set are also discussed. The method is based on the application of a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces. The approach is new even for the case of the metric spaces. As an application, an existence result for a mixed boundary and initial value problem for a system of second order differential inclusions is given. [ABSTRACT FROM AUTHOR]

Several iterative processes have been defined by researchers to approximate the fixed points of various classes operators. In this paper we present, by using the basins of attraction for the roots of some complex polynomials, an empirical comparison of some iteration procedures for fixed points approximation of Newton's iteration operator. Some numerical results are presented. The Matlab m-files for generating the basins of attraction are presented, too. [ABSTRACT FROM AUTHOR]

In this paper we study the properties of the common fixed points set of a commuting family of monotone nonexpansive mappings in Banach spaces endowed with a graph. In particular, we prove that under certain conditions, this set is a monotone nonexpansive retract. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of operators, for which a fixed point theorem is proven. This class of mappings is very large and unifies several classes of contractive type operators from the literature, including Berinde mappings. Such fact is proven via a comparison with various metrical contractive type mappings. [ABSTRACT FROM AUTHOR]